Exhibit 10.2

       

      SUBORDINATED NOTE

       

      GREENE COUNTY BANCORP, INC.

      3.00% FIXED-TO-FLOATING RATE SUBORDINATED NOTE DUE SEPTEMBER 15, 2031

       

      THE INDEBTEDNESS EVIDENCED BY THIS SUBORDINATED NOTE IS SUBORDINATED AND JUNIOR IN RIGHT OF PAYMENT TO SENIOR INDEBTEDNESS (AS DEFINED IN SECTION 3 OF THIS SUBORDINATED NOTE) OF GREENE COUNTY BANCORP, INC.
        (THE “COMPANY”), INCLUDING OBLIGATIONS OF THE COMPANY TO ITS GENERAL CREDITORS AND SECURED CREDITORS, AND IS UNSECURED.  IT IS INELIGIBLE AS COLLATERAL FOR ANY EXTENSION OF CREDIT BY THE COMPANY OR ANY OF ITS SUBSIDIARIES.  IN THE EVENT OF
        LIQUIDATION, ALL HOLDERS OF SENIOR INDEBTEDNESS OF THE COMPANY SHALL BE ENTITLED TO BE PAID IN FULL WITH SUCH INTEREST AS MAY BE PROVIDED BY LAW BEFORE ANY PAYMENT SHALL BE MADE ON ACCOUNT OF PRINCIPAL OF OR INTEREST ON THIS SUBORDINATED NOTE. 
        AFTER PAYMENT IN FULL OF ALL SUMS OWING TO SUCH HOLDERS OF SENIOR INDEBTEDNESS, THE HOLDER OF THIS SUBORDINATED NOTE, TOGETHER WITH THE HOLDERS OF ANY OBLIGATIONS OF THE COMPANY RANKING ON A PARITY WITH THE SUBORDINATED NOTES, SHALL BE ENTITLED TO
        BE PAID FROM THE REMAINING ASSETS OF THE COMPANY THE UNPAID PRINCIPAL AMOUNT OF THIS SUBORDINATED NOTE PLUS ACCRUED AND UNPAID INTEREST THEREON BEFORE ANY PAYMENT OR OTHER DISTRIBUTION, WHETHER IN CASH, PROPERTY OR OTHERWISE, SHALL BE MADE (I) WITH
        RESPECT TO ANY OBLIGATION THAT BY ITS TERMS EXPRESSLY IS JUNIOR IN THE RIGHT OF PAYMENT TO THE SUBORDINATED NOTES, (II) WITH RESPECT TO ANY INDEBTEDNESS BETWEEN THE COMPANY AND ANY OF ITS SUBSIDIARIES OR AFFILIATES, OR (III) ON ACCOUNT OF ANY
        SHARES OF CAPITAL STOCK OF THE COMPANY.

       

      THE INDEBTEDNESS EVIDENCED BY THIS SUBORDINATED NOTE IS NOT A DEPOSIT AND IS NOT INSURED BY THE FEDERAL DEPOSIT INSURANCE CORPORATION OR ANY OTHER GOVERNMENT AGENCY OR FUND.

       

      THIS SUBORDINATED NOTE WILL BE ISSUED AND MAY BE TRANSFERRED ONLY IN MINIMUM DENOMINATIONS OF $250,000 AND MULTIPLES OF $1,000 IN EXCESS THEREOF.  ANY ATTEMPTED TRANSFER OF THIS SUBORDINATED NOTE IN A DENOMINATION OF
        LESS THAN $1,000 SHALL BE DEEMED TO BE VOID AND OF NO LEGAL EFFECT WHATSOEVER.  ANY SUCH PURPORTED TRANSFEREE SHALL BE DEEMED NOT TO BE THE HOLDER OF THIS SUBORDINATED NOTE FOR ANY PURPOSE, INCLUDING, BUT NOT LIMITED TO, THE RECEIPT OF PAYMENTS ON
        THIS SUBORDINATED NOTE, AND SUCH PURPORTED TRANSFEREE SHALL BE DEEMED TO HAVE NO INTEREST WHATSOEVER IN THIS SUBORDINATED NOTE.

       

      
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      THIS SUBORDINATED NOTE MAY BE SOLD ONLY IN COMPLIANCE WITH APPLICABLE FEDERAL AND STATE SECURITIES LAWS.  THIS SUBORDINATED NOTE HAS NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE “SECURITIES

          ACT”), OR ANY APPLICABLE STATE SECURITIES LAWS OR ANY OTHER APPLICABLE SECURITIES LAWS.  NEITHER THIS SUBORDINATED NOTE NOR ANY INTEREST OR PARTICIPATION HEREIN MAY BE REOFFERED, SOLD, ASSIGNED, TRANSFERRED, PLEDGED, ENCUMBERED OR OTHERWISE
        DISPOSED OF IN THE ABSENCE OF SUCH REGISTRATION OR UNLESS SUCH TRANSACTION IS EXEMPT FROM, OR NOT SUBJECT TO, THE REGISTRATION REQUIREMENTS OF THE SECURITIES ACT.

       

      CERTAIN ERISA CONSIDERATIONS:

      

      

      THE HOLDER OF THIS SUBORDINATED NOTE, OR ANY INTEREST HEREIN, BY ITS ACCEPTANCE HEREOF OR THEREOF AGREES, REPRESENTS AND WARRANTS THAT IT IS NOT AN EMPLOYEE BENEFIT PLAN, INDIVIDUAL RETIREMENT ACCOUNT OR OTHER PLAN
        OR ARRANGEMENT SUBJECT TO TITLE I OF THE EMPLOYEE RETIREMENT INCOME SECURITY ACT OF 1974, AS AMENDED (“ERISA”), OR SECTION 4975 OF THE INTERNAL REVENUE CODE OF 1986, AS AMENDED (THE “CODE”) (EACH A “PLAN”), OR AN ENTITY WHOSE
        UNDERLYING ASSETS INCLUDE “PLAN ASSETS” BY REASON OF ANY PLAN’S INVESTMENT IN THE ENTITY, AND NO PERSON INVESTING “PLAN ASSETS” OF ANY PLAN MAY ACQUIRE OR HOLD THIS SUBORDINATED NOTE OR ANY INTEREST HEREIN, UNLESS SUCH PURCHASER OR HOLDER IS
        ELIGIBLE FOR THE EXEMPTIVE RELIEF AVAILABLE UNDER U.S. DEPARTMENT OF LABOR PROHIBITED TRANSACTION CLASS EXEMPTION 96-23, 95-60, 91-38, 90-1 OR 84-14 OR ANOTHER APPLICABLE EXEMPTION OR ITS PURCHASE AND HOLDING OF THIS SUBORDINATED NOTE, OR ANY
        INTEREST HEREIN, ARE NOT PROHIBITED BY SECTION 406 OF ERISA OR SECTION 4975 OF THE CODE WITH RESPECT TO SUCH PURCHASE AND HOLDING. ANY PURCHASER OR HOLDER OF THIS SUBORDINATED NOTE OR ANY INTEREST HEREIN WILL BE DEEMED TO HAVE REPRESENTED BY ITS
        PURCHASE AND HOLDING THEREOF THAT EITHER: (I) IT IS NOT AN EMPLOYEE BENEFIT PLAN OR OTHER PLAN TO WHICH TITLE I OF ERISA OR SECTION 4975 OF THE CODE IS APPLICABLE, A TRUSTEE OR OTHER PERSON ACTING ON BEHALF OF ANY SUCH EMPLOYEE BENEFIT PLAN OR
        PLANS, OR ANY OTHER PERSON OR ENTITY USING THE “PLAN ASSETS” OF ANY SUCH EMPLOYEE BENEFIT PLAN OR PLANS TO FINANCE SUCH PURCHASE OR (II) SUCH PURCHASE OR HOLDING WILL NOT RESULT IN A PROHIBITED TRANSACTION UNDER SECTION 406 OF ERISA OR SECTION 4975
        OF THE CODE FOR WHICH FULL EXEMPTIVE RELIEF IS NOT AVAILABLE UNDER APPLICABLE STATUTORY OR ADMINISTRATIVE EXEMPTION.

       

      ANY FIDUCIARY OF ANY PLAN WHO IS CONSIDERING THE ACQUISITION OF THIS SUBORDINATED NOTE OR ANY INTEREST HEREIN SHOULD CONSULT WITH HIS OR HER LEGAL COUNSEL PRIOR TO ACQUIRING THIS SUBORDINATED NOTE
        OR ANY INTEREST HEREIN.

       

      
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      No. 0XX

      

      

      GREENE COUNTY BANCORP, INC.

       

      3.00% FIXED-TO-FLOATING RATE SUBORDINATED NOTE DUE 

       

      SEPTEMBER 15, 2031

       

      1.          Subordinated Notes.  This Subordinated Note is one of an issue of notes of Greene County Bancorp, Inc., a federal corporation (the “Company”)

        designated as the “3.00% Fixed-to-Floating Rate Subordinated Notes due September 15, 2031” (the “Subordinated Notes”) issued pursuant to that Subordinated Note Purchase Agreement, dated as of September 15, 2031 by and among the Company and
        the several purchasers of the Subordinated Notes identified on the signature pages thereto (the “Purchase Agreement”).

       

      2.          Payment.  The Company, for value received, promises to pay to _____________________, or its registered assigns, the principal sum of [⸱]
        Dollars (U.S.) ($[⸱]), plus accrued but unpaid interest on September 15, 2031 (“Stated Maturity”) and to pay interest thereon (i) from and including September 15, 2021 (the “Issue Date”) to but excluding September 15, 2026 or the earlier
        redemption date contemplated by Section 4 of this Subordinated Note, at the rate of 3.00% per annum, computed on the basis of a 360-day year consisting of twelve 30-day months and payable semi-annually in arrears on March 15 and September
        15 of each year (each payment date, a “Fixed Rate Interest Payment Date”), and (ii) from and including September 15, 2026 to but excluding the Stated Maturity or the earlier redemption date contemplated by Section 4 of this
        Subordinated Note, at the rate per annum, reset quarterly, equal to the Floating Interest Rate (as defined below) determined on the Floating Interest Determination Date (as defined below) of the applicable interest period plus 295 basis points, provided, that in the event the Floating Interest Rate is less than zero, then the Floating Interest Rate shall be deemed to be zero, computed on the basis of a 360-day year and the actual number of days
        elapsed and payable quarterly in arrears (each quarterly period, a “Floating Rate Period”) on January 1, April 1, July 1 and October 1 of each year (each payment date, a “Floating Rate Interest Payment Date”).  Dollar amounts
        resulting from this calculation shall be rounded to the nearest cent, with one-half cent being rounded up. The term “Floating Interest Determination Date” means the date upon which the Floating Interest Rate is determined by the Calculation
        Agent (as defined below) pursuant to the Three-Month Term SOFR Conventions (as defined below).  Any payment of principal of or interest on this Subordinated Note that would otherwise become due and payable on a day which is not a Business Day shall
        become due and payable on the next succeeding Business Day, with the same force and effect as if made on the date for payment of such principal or interest, and no interest will accrue in respect of such payment for the period after such day;
        provided, that in the event that any scheduled Floating Rate Interest Payment Date falls on a day that is not a Business Day and the next succeeding Business Day falls in the next succeeding calendar month, such Floating Rate Interest Payment Date
        will be accelerated to the immediately preceding Business Day, and, in each such case, the amounts payable on such Business Day will include interest accrued to, but excluding, such Business Day.  Dollar amounts resulting from interest calculations
        will be rounded to the nearest cent, with one half cent being rounded upward.

       

      
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      (a)          The Company shall take such actions as are necessary to ensure that from the commencement of the Floating Rate Period for so long as any of
        the Subordinated Notes remain outstanding there will at all times be a Calculation Agent appointed to calculate Three-Month Term SOFR in respect of each Floating Rate Period. The calculation of Three-Month Term SOFR for each applicable Floating
        Rate Period by the Calculation Agent will (in the absence of manifest error) be final and binding. The Calculation Agent’s determination of any interest rate and its calculation of interest payments for any period will be maintained on file at the
        Calculation Agent’s principal offices and will be made available to any Noteholder (as defined below) upon request. The Calculation Agent may be removed by the Company at any time. If the Calculation Agent is unable or unwilling to act as
        Calculation Agent or is removed by the Company, the Company will promptly appoint a replacement Calculation Agent. The Calculation Agent may not resign its duties without a successor having been duly appointed; provided, that if a successor
        Calculation Agent has not been appointed by the Company and such successor accepted such position within thirty (30) days after the giving of notice of resignation by the Calculation Agent, then the resigning Calculation Agent may petition, at the
        expense of the Company, any court of competent jurisdiction for the appointment of a successor Calculation Agent with respect to such series. For the avoidance of doubt, if at any time there is no Calculation Agent appointed by the Company, then
        the Company shall be the Calculation Agent.

       

      (b)          An “Interest Payment Date” is either a Fixed Rate Interest Payment Date or a Floating Rate Interest Payment Date, as applicable.

       

      (c)          The “Floating Interest Rate” means:

       

      (i)          initially Three-Month Term SOFR (as defined below).

       

      (ii)          Notwithstanding the foregoing clause (i) of this Section 2(c):

       

      (1)         If the Calculation Agent determines prior to the relevant Floating Interest Determination Date that a Benchmark Transition Event and its
        related Benchmark Replacement Date (each of such terms as defined below) have occurred with respect to Three-Month Term SOFR, then the Company shall promptly provide notice of such determination to the Noteholders and Section 2(d) will
        thereafter apply to all determinations, calculations and quotations made or obtained for the purposes of calculating the Floating Interest Rate payable on the Subordinated Notes during a relevant Floating Rate Period.

       

      (2)        However, if the Calculation Agent determines that a Benchmark Transition Event and its related Benchmark Replacement Date have occurred with
        respect to Three-Month Term SOFR, but for any reason the Benchmark Replacement has not been determined as of the relevant Floating Interest Determination Date, the Floating Interest Rate for the applicable Floating Rate Period will be equal to the
        Floating Interest Rate on the last Floating Interest Determination Date for the Subordinated Notes, as determined by the Calculation Agent.

       

      
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      (d)         Effect of Benchmark Transition Event.

       

      (i)          If the Calculation Agent determines that a Benchmark Transition Event and its related Benchmark Replacement Date have occurred prior to the
        Reference Time (as defined below) in respect of any determination of the Benchmark (as defined below) on any date, the Benchmark Replacement will replace the then-current Benchmark for all purposes relating to the Subordinated Notes during the
        relevant Floating Rate Period in respect of such determination on such date and all determinations on all subsequent dates.

       

      (ii)        In connection with the implementation of a Benchmark Replacement, the Calculation Agent will have the right to make Benchmark Replacement
        Conforming Changes from time to time, and such changes shall become effective without consent from the Noteholders or any other party.

       

      (iii)       The Calculation Agent is expressly authorized to make certain determinations, decisions and elections under the Subordinated Notes, including
        with respect to the use of Three-Month Term SOFR as the Benchmark under this Section 2(d).  Any determination, decision or election that may be made by the Calculation Agent under the terms of the Subordinated Notes, including any
        determination with respect to a tenor, rate or adjustment or of the occurrence or non-occurrence of an event, circumstance or date, and any decision to take or refrain from taking any action or any selection:

       

      (1)          will be conclusive and binding absent manifest error;

       

      (2)          if made by the Company as the Calculation Agent, will be made in the Company’s sole discretion;

       

      (3)          if made by the Calculation Agent other than the Company, will be made after consultation with the Company, and the Calculation Agent will not
        make any such determination, decision or election to which the Company reasonably objects; and

       

      (4)         notwithstanding anything to the contrary in this Subordinated Note or the Purchase Agreement, shall become effective without consent from the
        Noteholders or any other party.

       

      (iv)          If the Calculation Agent fails to make any determination, decision or election that it is required to make
          under the terms of the Subordinated Notes, then the Company will make such determination, decision or election on the same basis as described above.

       

      (v)          For the avoidance of doubt, after a Benchmark Transition Event and its related Benchmark Replacement Date have occurred, interest payable on
        this Subordinated Note for the Floating Rate Period will be an annual rate equal to the sum of the applicable Benchmark Replacement plus 295 basis points.

       

      (vi)      If the then-current Benchmark is Three-Month Term SOFR, the Calculation Agent will have the right to establish the Three-Month Term SOFR
        Conventions, and if any of the foregoing provisions concerning the calculation of the interest rate and the payment of interest during the Floating Rate Period are inconsistent with any of the Three-Month Term SOFR Conventions determined by the
        Calculation Agent, then the Three-Month Term SOFR Conventions as determined by the Calculation Agent will apply.

       

      (vii)        As used in this Subordinated Note:

       

      
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      (1)          “Benchmark” means, initially, Three-Month Term SOFR; provided that if the Calculation Agent determines on or prior to the Reference
        Time that a Benchmark Transition Event and its related Benchmark Replacement Date have occurred with respect to Three-Month Term SOFR or the then-current Benchmark, then “Benchmark” means the applicable Benchmark Replacement.

       

      (2)         “Benchmark Replacement” means the Interpolated Benchmark with respect to the then-current Benchmark; provided that if (a) the
        Calculation Agent cannot determine the Interpolated Benchmark as of the Benchmark Replacement Date or (b) the then-current Benchmark is Three-Month Term SOFR and a Benchmark Transition Event and its related Benchmark Replacement Date have occurred
        with respect to Three-Month Term SOFR (in which event no Interpolated Benchmark with respect to Three-Month Term SOFR shall be determined), then “Benchmark Replacement” means the first alternative set forth in the order below that can be
        determined by the Calculation Agent as of the Benchmark Replacement Date:

       

      a.          the sum of: (i) Compounded SOFR and (ii) the Benchmark Replacement Adjustment;

       

      b.      the sum of: (i) the alternate rate of interest that has been selected or recommended by the Relevant Governmental Body as the replacement for the
        then-current Benchmark for the applicable Corresponding Tenor and (ii) the Benchmark Replacement Adjustment;

       

      c.          the sum of: (i) the ISDA Fallback Rate and (ii) the Benchmark Replacement Adjustment;

       

      d.        the sum of: (i) the alternate rate of interest that has been selected by the Calculation Agent as the replacement for the then-current Benchmark
        for the applicable Corresponding Tenor giving due consideration to any industry-accepted rate of interest as a replacement for the then-current Benchmark for U.S. dollar denominated floating rate securities at such time and (ii) the Benchmark
        Replacement Adjustment.

       

      (3)         “Benchmark Replacement Adjustment” means the first alternative set forth in the order below that can be determined by the Calculation
        Agent as of the Benchmark Replacement Date:

       

      a.        the spread adjustment, or method for calculating or determining such spread adjustment, (which may be a positive or negative value or zero) that
        has been selected or recommended by the Relevant Governmental Body for the applicable Unadjusted Benchmark Replacement;

       

      b.        if the applicable Unadjusted Benchmark Replacement is equivalent to the ISDA Fallback Rate, then the ISDA Fallback Adjustment;

       

      c.       the spread adjustment (which may be a positive or negative value or zero) that has been selected by the Calculation Agent giving due
        consideration to any industry-accepted spread adjustment, or method for calculating or determining such spread adjustment, for the replacement of the then-current Benchmark with the applicable Unadjusted Benchmark Replacement for U.S. dollar
        denominated floating rate securities at such time.

       

      
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      (4)          “Benchmark Replacement Conforming Changes” means, with respect to any Benchmark Replacement, any technical, administrative or
        operational changes (including changes to the definition of  “Floating Rate Period,” timing and frequency of determining rates with respect to each Floating Rate Period and making payments of interest, rounding of amounts or tenors, and other
        administrative matters) that the Calculation Agent decides may be appropriate to reflect the adoption of such Benchmark Replacement in a manner substantially consistent with market practice (or, if the Calculation Agent decides that adoption of any
        portion of such market practice is not administratively feasible or if the Calculation Agent determines that no market practice for use of the Benchmark Replacement exists, in such other manner as the Calculation Agent determines is reasonably
        necessary).

       

      (5)        “Benchmark Replacement Date” means the earliest to occur of the following events with respect to the then-current Benchmark:

       

      a.          in the case of clause (a) of the definition of “Benchmark Transition Event,” the relevant Reference Time in respect of any
        determination; or

       

      b.          in the case of clause (b) or (c) of the definition of “Benchmark Transition Event,” the later of (i) the date of the public
        statement or publication of information referenced therein and (ii) the date on which the administrator of the Benchmark permanently or indefinitely ceases to provide the Benchmark; or

       

      c.          in the case of clause (d) of the definition of “Benchmark Transition Event,” the date of the
        public statement or publication of information referenced therein.

       

      For the avoidance of doubt, for purposes of the definitions of Benchmark Replacement Date and Benchmark Transition Event, references to the Benchmark also include any reference
        rate underlying the Benchmark (for example, if the Benchmark becomes Compounded SOFR, references to the Benchmark would include SOFR).

       

      For the avoidance of doubt, if the event giving rise to the Benchmark Replacement Date occurs on the same day as, but earlier than, the Reference Time in respect of any determination, the Benchmark
        Replacement Date will be deemed to have occurred prior to the Reference Time for such determination.

       

      (6)          “Benchmark Transition Event” means the occurrence of one or more of the following events with respect to the then-current Benchmark:

       

      a.       if the Benchmark is Three-Month Term SOFR, (i) the Relevant Governmental Body has not selected or recommended a forward-looking term rate for a
        tenor of three months based on SOFR, (ii) the development of a forward-looking term rate for a tenor of three months based on SOFR that has been recommended or selected by the Relevant Governmental Body is not complete or (iii) the Company
        determines that use of a forward-looking rate for a tenor of three months based on SOFR is not administratively feasible;

       

      
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      b.       a public statement or publication of information by or on behalf of the administrator of the Benchmark announcing that such administrator has
        ceased or will cease to provide the Benchmark, permanently or indefinitely, provided that, at the time of such statement or publication, there is no successor administrator that will continue to provide the Benchmark;

       

      c.       a public statement or publication of information by the regulatory supervisor for the administrator of the Benchmark, the central bank for the
        currency of the Benchmark, an insolvency official with jurisdiction over the administrator for the Benchmark, a resolution authority with jurisdiction over the administrator for the Benchmark or a court or an entity with similar insolvency or
        resolution authority over the administrator for the Benchmark, which states that the administrator of the Benchmark has ceased or will cease to provide the Benchmark permanently or indefinitely, provided that, at the time of such statement or
        publication, there is no successor administrator that will continue to provide the Benchmark; or

       

      d.       a public statement or publication of information by the regulatory supervisor for the administrator of the Benchmark announcing that the
        Benchmark is no longer representative.

       

      (7)           “Business Day” means any day that is not a Saturday or Sunday and that is not a day on which is a federal legal holiday in the United
        States.

       

      (8)           “Calculation Agent” means the agent (which may be the Company or an affiliate of the Company) as may be appointed by the Company to
        act as Calculation Agent for the Subordinated Notes prior to the commencement of the Floating Rate Period to act in accordance with Section 2.

       

      (9)          “Compounded SOFR” means the compounded average of SOFRs for the applicable Corresponding Tenor, with the rate, or methodology for this
        rate, and conventions for this rate being established by the Calculation Agent in accordance with:

       

      a.          the rate, or methodology for this rate and conventions for this rate selected or recommended by the Relevant Governmental Body for determining
        compounded SOFR; provided that:

       

      b.         if, and to the extent that, the Calculation Agent determines that Compounded SOFR cannot be determined in accordance with clause (a)
        above, then the rate, or methodology for this rate, and conventions for this rate that have been selected by the Calculation Agent giving due consideration to any industry-accepted market practice for U.S. dollar denominated floating rate
        securities at such time.

       

      For the avoidance of doubt, the calculation of Compounded SOFR will exclude the Benchmark Replacement Adjustment plus 295 basis points.

       

      (10)       “Corresponding Tenor” with respect to a Benchmark Replacement means a tenor (including overnight) having approximately the same length
        (disregarding Business Day adjustment) as the applicable tenor for the then-current Benchmark.

       

      
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      (11)          “FRBNY” means the Federal Reserve Bank of New York.

       

      (12)          “FRBNY’s Website” means the website of the FRBNY at http://www.newyorkfed.org, or any successor source.

       

      (13)         “Interpolated Benchmark” with respect to the Benchmark means the rate determined for the Corresponding Tenor by interpolating on a
        linear basis between: (1) the Benchmark for the longest period (for which the Benchmark is available) that is shorter than the Corresponding Tenor and (2) the Benchmark for the shortest period (for which the Benchmark is available) that is longer
        than the Corresponding Tenor.

       

      (14)          “ISDA” means the International Swaps and Derivatives Association, Inc. or any successor thereto.

       

      (15)          “ISDA Definitions” means the 2006 ISDA Definitions published by the ISDA or any successor thereto, as amended or supplemented from
        time to time, or any successor definitional booklet for interest rate derivatives published from time to time.

       

      (16)          “ISDA Fallback Adjustment” means the spread adjustment (which may be a positive or negative value or zero) that would apply for
        derivatives transactions referencing the ISDA Definitions to be determined upon the occurrence of an index cessation event with respect to the Benchmark for the applicable tenor.

       

      (17)        “ISDA Fallback Rate” means the rate that would apply for derivatives transactions referencing the ISDA Definitions to be effective upon
        the occurrence of an index cessation date with respect to the Benchmark for the applicable tenor excluding the applicable ISDA Fallback Adjustment.

       

      (18)          “Reference Time” with respect to any determination of the Benchmark means (a) if the Benchmark is Three-Month Term SOFR, the time
        determined by the Calculation Agent after giving effect to the Three-Month Term SOFR Conventions, and (b) if the Benchmark is not Three-Month Term SOFR, the time determined by the Calculation Agent after giving effect to the Benchmark Replacement
        Conforming Changes.

       

      (19)       “Relevant Governmental Body” means the Board of Governors of the Federal Reserve System (the “Federal Reserve”) and/or the FRBNY,
        or a committee officially endorsed or convened by the Federal Reserve and/or the FRBNY or any successor thereto.

       

      (20)        “SOFR” means the daily secured overnight financing rate published by the FRBNY, as the administrator of the benchmark, (or a successor
        administrator) on the FRBNY’s Website (or such successor’s website).

       

      (21)         “Term SOFR” means the forward-looking term rate for the applicable Corresponding Tenor based on SOFR that has been selected or
        recommended by the Relevant Governmental Body.

       

      
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      (22)          “Term SOFR Administrator” means any entity designated by the Relevant Governmental Body as the administrator of Term SOFR (or
        successor administrator).

       

      (23)        “Three-Month Term SOFR” means the rate for Term SOFR for a tenor of three months that is published by the Term SOFR Administrator at
        the Reference Time for any Floating Rate Period, as determined by the Calculation Agent after giving effect to the Three-Month Term SOFR Conventions. All percentages used in or resulting from any calculation of Three-Month Term SOFR shall be
        rounded, if necessary, to the nearest one-hundred-thousandth of a percentage point, with 0.000005% rounded up to 0.00001%.

       

      (24)      “Three-Month Term SOFR Conventions” means any determination, decision or election with respect to any technical, administrative or
        operational matter (including with respect to the manner and timing of the publication of Three-Month Term SOFR, or changes to the definition of “Floating Rate Period”, timing and frequency of determining Three-Month Term SOFR with respect to each
        Floating Rate Period and making payments of interest, rounding of amounts or tenors, and other administrative matters) that the Calculation Agent decides may be appropriate to reflect the use of Three-Month Term SOFR as the Benchmark in a manner
        substantially consistent with market practice (or, if the Calculation Agent decides that adoption of any portion of such market practice is not administratively feasible or if the Calculation Agent determines that no market practice for the use of
        Three-Month Term SOFR exists, in such other manner as the Calculation Agent determines is reasonably necessary).

       

      (25)          “Unadjusted Benchmark Replacement” means the Benchmark Replacement excluding the Benchmark Replacement Adjustment.

       

      3.          Subordination.

       

      (a)          The indebtedness of the Company evidenced by this Subordinated Note, including the principal and interest on this Subordinated Note, shall be
        subordinate and junior in right of payment to the prior payment in full of all existing claims of creditors of the Company whether now outstanding or subsequently created, assumed, guaranteed or incurred (collectively, “Senior Indebtedness”),

        which shall consist of principal of (and premium, if any) and interest, if any, on: (i) all indebtedness and obligations of, or guaranteed or assumed by, the Company for money borrowed, whether or not evidenced by bonds, debentures, securities,
        notes or other similar instruments, and including, but not limited to, all obligations to the Company’s general creditors and secured creditors; (ii) any deferred obligations of the Company for the payment of the purchase price of property or
        assets acquired other than in the ordinary course of business; (iii) all obligations, contingent or otherwise, of the Company in respect of any letters of credit, bankers’ acceptances, security purchase facilities and similar direct credit
        substitutes; (iv) any capital lease obligations of the Company; (v) all obligations of the Company in respect of interest rate swap, cap or other agreements, interest rate future or option contracts, currency swap agreements, currency future or
        option contracts, commodity contracts and other similar arrangements or derivative products; (vi) any obligation of the Company to its general creditors, as defined for purposes of the capital adequacy regulations of the Federal Reserve applicable
        to the Company, as the same may be amended or modified from time to time; (vii) all obligations that are similar to those in clauses (i) through (vi) of other persons for the payment of which the Company is responsible or liable as obligor,
        guarantor or otherwise arising from an off-balance sheet guarantee; (viii) all obligations of the types referred to in clauses (i) through (vii) of other persons secured by a lien on any property or asset of the Company; and (ix) in the case of (i)
        through (viii) above, all amendments, renewals, extensions, modifications and refundings of such indebtedness and obligations; except “Senior Indebtedness” does not include (A) the Subordinated Notes, (B)
        any obligation that by its terms expressly is junior to, or ranks equally in right of payment with, the Subordinated Notes, including the Company’s existing 4.75% fixed-to-floating rate subordinated notes due 2030, or (C) any indebtedness between
        the Company and any of its subsidiaries or Affiliates.  This Subordinated Note is not secured by any assets of the Company or any subsidiary or Affiliate of the Company.  The term “Affiliate(s)” means, with respect to any Person (as such
        term is defined in the Purchase Agreement), such Person’s immediate family members, partners, members or parent and subsidiary corporations, and any other Person directly or indirectly controlling, controlled by, or under common control with said
        Person and their respective Affiliates.

       

      
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      (b)          In the event of any liquidation of the Company, holders of Senior Indebtedness of the Company shall be entitled to be paid in full with such
        interest as may be provided by law before any payment shall be made on account of principal of or interest on this Subordinated Note.  Additionally, in the event of any insolvency, dissolution, assignment for the benefit of creditors or any
        liquidation or winding up of or relating to the Company, whether voluntary or involuntary, holders of Senior Indebtedness shall be entitled to be paid in full before any payment shall be made on account of the principal of or interest on the
        Subordinated Notes, including this Subordinated Note.  In the event of any such proceeding, after payment in full of all sums owing with respect to the Senior Indebtedness, the registered holders of the Subordinated Notes from time to time (each a
        “Noteholder” and, collectively, the “Noteholders”), together with the holders of any obligations of the Company ranking on a parity with the Subordinated Notes, shall be entitled to be paid from the remaining assets of the Company the
        unpaid principal thereof, and the unpaid interest thereon before any payment or other distribution, whether in cash, property or otherwise, shall be made (i) with respect to any obligation that by its terms expressly is junior to in the right of
        payment to the Subordinated Notes, (ii) with respect to any indebtedness between the Company and any of its subsidiaries or Affiliates or (iii) on account of any capital stock.

       

      (c)         If there shall have occurred and be continuing (i) a default in any payment with respect to any Senior Indebtedness or (ii) an event of default
        with respect to any Senior Indebtedness as a result of which the maturity thereof is accelerated, unless and until such payment default or event of default shall have been cured or waived or shall have ceased to exist, no payments shall be made by
        the Company with respect to the Subordinated Notes, notwithstanding the provisions of Section 18 hereof.  The provisions of this paragraph shall not apply to any payment with respect to which Section 3(b) above would be applicable.

       

      (d)         Nothing herein shall act to prohibit, limit or impede the Company from issuing additional debt of the Company having the same rank as the
        Subordinated Notes or which may be junior or senior in rank to the Subordinated Notes.  Each Noteholder, by its acceptance hereof, agrees to and shall be bound by the provisions of this Section 3.  Each Noteholder, by its acceptance hereof,
        further acknowledges and agrees that the foregoing subordination provisions are, and are intended to be, an inducement and a consideration for each holder of any Senior Indebtedness, whether such Senior Indebtedness was created or acquired before
        or after the issuance of the Subordinated Notes, to acquire and continue to hold, or to continue to hold, such Senior Indebtedness, and such holder of Senior Indebtedness shall be deemed conclusively to have relied on such subordination provisions
        in acquiring and continuing to hold or in continuing to hold such Senior Indebtedness.

       

      
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      4.          Redemption.

       

      (a)        Redemption Prior to Fifth Anniversary.  This Subordinated Note shall not be redeemable by the Company in whole or in part prior to the
        fifth anniversary of the Issue Date, except in the event of: (i) a Tax Event (as defined below); (ii) an Investment Company Event (as defined below); or (iii) in the event that the Company and its parent mutual holding company, Greene County
        Bancorp, MHC, consummate a second-step mutual to stock conversion pursuant to the regulations of the Federal Reserve Board (12 CFR § 239 et seq.) (a “Conversion Transaction”).  Upon the occurrence of a Tax
        Event, an Investment Company Event or a Conversion Transaction, subject to Section 4(f) below, the Company may redeem this Subordinated Note in whole, but not in part, at any time, upon giving not less than 10 calendar days’ notice to the
        Noteholders at an amount equal to 100% of the outstanding principal amount being redeemed plus accrued and unpaid interest, to but excluding the redemption date.  “Tax Event” means the receipt by the Company of an opinion of counsel to the
        Company that as a result of any amendment to, or change (including any final and adopted (or enacted) prospective change) in, the laws (or any regulations thereunder) of the United States or any political subdivision or taxing authority thereof or
        therein, or as a result of any official administrative pronouncement or judicial decision interpreting or applying such laws or regulations, there is a material risk that interest payable by the Company on the Subordinated Notes is not, or within
        120 days after the receipt of such opinion will not be, deductible by the Company, in whole or in part, for United States federal income tax purposes.  “Investment Company Event” means the receipt by the Company of an opinion of counsel to
        the Company to the effect that there is a material risk that the Company is or, within 120 days after the receipt of such opinion will be, required to register as an investment company pursuant to the Investment Company Act of 1940, as amended.

       

      (b)       Redemption on or after Fifth Anniversary.  On or after the fifth anniversary of the Issue Date, subject to Section 4(f) below,
        this Subordinated Note shall be redeemable at the option of and by the Company, in whole or in part at any time and from time to time upon any Interest Payment Date, at an amount equal to 100% of the outstanding principal amount being redeemed plus
        accrued but unpaid interest, to but excluding the redemption date, but in all cases in a principal amount with integral multiples of $1,000.  In addition, on or after the fifth anniversary of the Issue Date, subject to Section 4(f), the
        Company may redeem all or a portion of the Subordinated Notes, at any time upon the occurrence of a Tax Event, an Investment Company Event or a Conversion Transaction.

       

      (c)         Partial Redemption.   If less than the then outstanding principal amount of this Subordinated Note is redeemed, (i) a new Subordinated
        Note shall be issued representing the unredeemed portion without charge to the holder thereof and (ii) such redemption shall be effected on a pro rata basis as to the Noteholders.  For purposes of clarity, upon a partial redemption, a like
        percentage of the principal amount of every Subordinated Note held by every Noteholder shall be redeemed.

       

      
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      (d)       No Redemption at Option of Noteholder.  This Subordinated Note is not subject to redemption at the option of the holder of this
        Subordinated Note.

       

      (e)        Effectiveness of Redemption.  If notice of redemption has been duly given and notwithstanding that this Subordinated Note has been
        called for redemption but has not yet been surrendered for cancellation, on and after the date fixed for redemption interest shall cease to accrue on the portion of this Subordinated Note called for redemption, this Subordinated Note shall no
        longer be deemed outstanding with respect to the portion called for redemption and all rights with respect to the portion of this Subordinated Note called for redemption shall forthwith on such date fixed for redemption cease and terminate unless
        the Company shall default in the payment of the redemption price, except only the right of the Noteholder to receive the amount payable on such redemption, without interest.

       

      (f)         Regulatory Approvals. Any such redemption shall be subject to receipt of any and all required federal and state regulatory approvals,
        including, but not limited to, the consent of the Federal Reserve.  In the case of any redemption of this Subordinated Note pursuant to paragraphs (b) of this Section 4, the Company will give the Noteholder notice of redemption, which
        notice shall indicate the aggregate principal amount of Subordinated Notes to be redeemed, not less than 30 nor more than 45 calendar days prior to the proposed redemption date.

       

      (g)        Purchase and Resale of the Subordinated Notes. Subject to any required federal and state regulatory approvals and the provisions of this
        Subordinated Note, the Company shall have the right to purchase any of the Subordinated Notes at any time in the open market, private transactions or otherwise.  If the Company purchases any Subordinated Notes, it may, in its discretion, hold,
        resell or cancel any of the purchased Subordinated Notes.

       

      5.          Events of Default; Acceleration.

       

      (a)          Each of the following events shall constitute an “Event of Default”:

       

      (i)        the entry of a decree or order for relief in respect of the Company by a court having jurisdiction in the premises in an involuntary case or
        proceeding under any applicable bankruptcy, insolvency, or reorganization law, now or hereafter in effect of the United States or any political subdivision thereof, and such decree or order will have continued unstayed and in effect for a period of
        90 consecutive days or a bank regulatory agency shall have placed the Bank into receivership;

       

      (ii)         the commencement by the Company of a voluntary case under any applicable bankruptcy, insolvency or reorganization law, now or hereafter in
        effect of the United States or any political subdivision thereof, or the consent by the Company to the entry of a decree or order for relief in an involuntary case or proceeding under any such law;

       

      
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      (iii)        the Company (A) becomes insolvent or is unable to pay its debts as they mature, (B) makes an assignment for the benefit of creditors, (C)
        admits in writing its inability to pay its debts as they mature, or (D) ceases to be a savings and loan holding company under the Home Owners’ Loan Act, as amended, except pursuant to a transaction whereby it becomes a bank holding company under
        the Bank Holding Company Act of 1956;

       

      (iv)       the failure of the Company to pay any installment of interest on any of the Subordinated Notes as and when the same will become due and payable,
        and the continuation of such failure for a period of 30 days;

       

      (v)          the failure of the Company to pay all or any part of the principal of any of the Subordinated Notes as and when the same will become due and
        payable;

       

      (vi)          the liquidation of the Company (for the avoidance of doubt, “liquidation” does not include any merger, consolidation, sale of equity or
        assets, second-step mutual to stock conversion or reorganization (exclusive of a reorganization in bankruptcy) of the Company or any of its subsidiaries);

       

      (vii)      the failure of the Company to perform any other covenant or agreement on the part of the Company contained in the Subordinated Notes, and the
        continuation of such failure for a period of 30 days after the date on which notice specifying such failure, stating that such notice is a “Notice of Default” hereunder and demanding that the Company remedy the same, will have been given, in the
        manner set forth in Section 22, to the Company by a Noteholder; or

       

      (viii)      the default by the Company under any bond, debenture, note or other evidence of indebtedness for money borrowed by the Company having an
        aggregate principal amount outstanding of at least $25,000,000, whether such indebtedness now exists or is created or incurred in the future, which default (A) constitutes a failure to pay any portion of the principal of such indebtedness when due
        and payable after the expiration of any applicable grace period or (B) results in such indebtedness becoming due or being declared due and payable prior to the date on which it otherwise would have become due and payable without, in the case of clause

          (A), such indebtedness having been discharged or, in the case of clause (B), without such indebtedness having been discharged or such acceleration having been rescinded or annulled.

       

      (b)          Unless the principal of this Subordinated Note already shall have become due and payable, if an Event of Default described in Section
          5(a)(i) or Section 5(a)(ii) shall have occurred and be continuing, Noteholders holding not less than twenty percent (20%) in aggregate principal amount of the Subordinated Notes at the time outstanding, by notice in writing to
        Company, may declare the principal amount of all outstanding Subordinated Notes to be due and payable immediately and, upon any such declaration, the same shall become and shall be immediately due and payable.  The Company waives demand,
        presentment for payment, notice of nonpayment, notice of protest, and all other notices.  Notwithstanding the foregoing, upon the occurrence of an Event of Default other than an Event of Default described in Section 5(a)(i) or Section
          5(a)(ii), the Noteholders may not accelerate the Stated Maturity of the Subordinated Notes and make the principal of, and any accrued and unpaid interest on, the Subordinated Notes, immediately due and payable.  The Company, within 30 calendar days after the receipt of written notice from any Noteholder of the occurrence of an Event of Default with respect to this Subordinated Note, shall notify all Noteholders, at their addresses
        shown on the Security Register (as defined in Section 14 below), of such written notice of Event of Default, unless such Event of Default shall have been cured or waived before the giving of such notice as certified by the Company in
        writing to the Noteholder or Noteholders who provided written notice of such Event of Default.

       

      
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      6.          Failure to Make Payments.  In the event of any failure by the Company to make any required payment of principal or interest on this
        Subordinated Note (and in the case of payment of interest, such failure to pay shall have continued for 30 calendar days), the Company will, upon demand of the Noteholders, pay to the Noteholders the amount then due and payable on this Subordinated
        Note for principal and interest (without acceleration of this Subordinated Note in any manner), with interest on the overdue principal and interest at the rate borne by this Subordinated Note, to the extent permitted by applicable law.  If the
        Company fails to pay such amount upon such demand, the Noteholders may, among other things, institute a judicial proceeding for the collection of the sums so due and unpaid, may prosecute such proceeding to judgment or final decree and may enforce
        the same against the Company and collect the amounts adjudged or decreed to be payable in the manner provided by law out of the property of the Company.

       

      Upon the occurrence of a failure by the Company to make any required payment of principal or interest on this Subordinated Note, or an Event of Default until such Event of Default is cured by the
        Company or waived pursuant to Section 17 of this Subordinated Note, the Company shall not, except as required by any federal or state governmental agency: (a) declare or pay any dividends or distributions on, or redeem, purchase, acquire, or make a
        liquidation payment with respect to, any of the Company’s capital stock; (b) make any payment of principal of or interest or premium, if any, on or repay, repurchase or redeem any indebtedness of the Company that ranks equal with or junior to the
        Subordinated Notes; or (c) make any payments under any guarantee that ranks equal with or junior to the Subordinated Notes, other than (i) any dividends or distributions in shares of, or options, warrants or rights to subscribe for or purchase
        shares of, any class of the Company’s common stock; (ii) any declaration of a non-cash dividend in connection with the implementation of a shareholders’ rights plan, or the issuance of stock under any such plan in the future, or the redemption or
        repurchase of any such rights pursuant thereto; (iii) as a result of a reclassification of the Company’s capital stock or the exchange or conversion of one class or series of the Company’s capital stock for another class or series of the Company’s
        capital stock; (iv) the purchase of fractional interests in shares of the Company’s capital stock pursuant to the conversion or exchange provisions of such capital stock or the security being converted or exchanged; or (v) purchases of any class of
        the Company’s common stock related to or from any benefit plans for the Company’s directors, officers or employees or any of the Company’s dividend reinvestment plans (the foregoing clauses (i) through (v) are collectively referred to as the “Permitted

          Dividends”).

       

      
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      7.          Affirmative Covenants of the Company.

       

      (a)          Notice of Certain Events.  To the extent permitted by applicable statute, rule or regulation, the Company shall provide written notice
        to the Noteholder of the occurrence of any of the following events as soon as practicable, but in no event later than fifteen (15) Business Days following the Company becoming aware of the occurrence of such event:

       

      (i)          The total risk-based capital ratio, Tier 1 risk-based capital ratio, common equity Tier 1 risk-based capital ratio or leverage ratio of the Company (but only to the extent the Company
        is required to measure and report such ratios on a consolidated basis under applicable law) or any of the Company’s banking subsidiaries, with regard to capital adequacy purposes and excluding the capital conservation buffer, becomes less than
        eight percent (8.0%), six percent (6.0%), four and one-half percent (4.50%) or four percent (4.0%), respectively;

       

      (ii)         The Company, or any of the Company’s subsidiaries, or any officer of the Company (in such capacity), becomes subject to any formal, written regulatory enforcement action (as defined by
        the applicable regulatory agency);

       

      (iii)         The ratio of non-performing assets to total assets of The Bank of Greene County (the “Bank”), as calculated by the Company in the ordinary course of business and consistent
        with past practices, becomes greater than four percent (4.0%);

       

      (iv)        The appointment, resignation, removal or termination of the chief executive officer, president, chief operating officer, chief financial officer  or any director of the Company
        (provided however that the Company reporting any such event on a Form 8-K filed with the Securities and Exchange Commission shall be deemed notice to the Noteholder); or

       

      (b)       Payment of Principal and Interest.  The Company covenants and agrees for the benefit of the Noteholders that it will duly and punctually
        pay the principal of, and interest on, this Subordinated Note, in accordance with the terms hereof.

       

      (c)         Maintenance of Office. The Company will maintain an office or agency in the city of Catskill, New York, where Subordinated Notes may be
        surrendered for registration of transfer or for exchange and where notices and demands to or upon the Company in respect of the Subordinated Notes may be served.  The Company may also from time to time designate one or more other offices or
        agencies where the Subordinated Notes may be presented or surrendered for any or all such purposes and may from time to time rescind such designations; provided that no such designation or rescission will in any manner relieve the Company of its
        obligation to maintain an office or agency in the city of Catskill, New York.  The Company will give prompt written notice to the Noteholders of any such designation or rescission and of any change in the location of any such other office or
        agency.

       

      
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      (d)         Corporate Existence. The Company will do or cause to be done all things necessary to preserve and keep in full force and effect: (i)
        the corporate existence of the Company; (ii) the existence (corporate or other) of each subsidiary; and (iii) the rights (charter and statutory), licenses and franchises of the Company and each of its subsidiaries; provided, however, that the
        Company will not be required to preserve the existence (corporate or other) of any of its subsidiaries or any such right, license or franchise of the Company or any of its subsidiaries if the Board of Directors of the Company determines that the
        preservation thereof is no longer desirable in the conduct of the business of the Company and its subsidiaries taken as a whole and that the loss thereof will not be disadvantageous in any material respect to the Noteholders; provided, further,
        that the Company may consummate a merger in which (i) the Company is the surviving entity or (ii) if the Company is not the surviving entity, the surviving entity assumes, by operation of law or otherwise, all of the obligations of the Company
        under the Subordinated Notes.

       

      (e)         Maintenance of Properties. The Company will, and will cause each subsidiary to, cause all its properties used or useful in the conduct
        of its business to be maintained and kept in good condition, repair and working order and supplied with all necessary equipment and will cause to be made all necessary repairs, renewals, replacements, betterments and improvements thereof, all as in
        the judgment of the Company may be necessary so that the business carried on in connection therewith may be properly and advantageously conducted at all times; provided, however, that nothing in this Section will prevent the Company or any
        subsidiary from discontinuing the operation and maintenance of any of their respective properties if such discontinuance is, in the judgment of the Board of Directors of the Company or of any subsidiary, as the case may be, desirable in the conduct
        of its business.

       

      (f)         Compliance Certificate.  The Company will deliver to the Noteholders, within (i) 45 days after the end of each of the first three
        fiscal quarters and (ii) 120 days after the end of each fiscal year, an Officer’s Certificate covering the preceding fiscal quarter or fiscal year, stating whether or not, to the best of his or her knowledge, the Company is in default in the
        performance and observance of any of the terms, provisions and conditions of this Subordinated Note (without regard to notice requirements or periods of grace) and if the Company will be in default, specifying all such defaults and the nature and
        status thereof of which he or she may have knowledge.

       

      (g)         [Reserved]

       

      (h)         Compliance with Laws.  The Company shall comply with the requirements of all laws, regulations, orders and decrees applicable to it or
        its properties, except for such noncompliance that would not reasonably be expected to have a Material Adverse Effect (as such term is defined in the Purchase Agreement) on the Company and its subsidiaries taken as a whole.

       

      (i)         Taxes and Assessments.  The Company shall punctually pay and discharge all material taxes, assessments, and other governmental charges
        or levies imposed upon it or upon its income or upon any of its properties; provided, that no such taxes, assessments or other governmental charges need be paid if they are being contested in good faith by the Company.

       

      (j)          Financial Statements; Access to Records.

       

      (i)          Not later than forty-five (45) days following the end of each fiscal quarter for which the Company has not submitted Parent Company Only
        Financial Statements for Small Holding Companies Reporting Form FR Y-9SP to the Federal Reserve, upon request, the Company shall provide the Noteholders with a copy of the Company’s unaudited parent company only balance sheet and statement of
        income (loss) for and as of the end of such immediately preceding fiscal quarter, prepared in accordance with past practice. Quarterly financial statements, if required herein, shall be unaudited and need not comply with GAAP.

       

      
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      (ii)          Not later than ninety (90) days from the end of each fiscal year, upon request the Company shall provide the Noteholder with copies of the
        Company’s audited financial statements consisting of the consolidated balance sheet of the Company as of the fiscal year end and the related statements of income (loss) and retained earnings, stockholders’ equity and cash flows for the fiscal year
        then ended.  Such financial statements shall be prepared in accordance with GAAP applied on a consistent basis throughout the period involved.

       

      8.          Negative Covenants of the Company.

       

      (a)         Limitation on Dividends.  The Company shall not declare or pay any dividend or make any distribution on capital stock or other equity
        securities of any kind of the Company if the Company is not “well capitalized” for regulatory capital purposes immediately prior to the declaration of such dividend or distribution, except for Permitted Dividends.

       

      (b)        Merger or Sale of Assets.  The Company shall not merge into another entity, effect a Change in Bank Control (as defined below), or
        convey, transfer or lease all or substantially all of  its properties and assets to any person, unless:

       

      (i)         the continuing entity into which the Company is merged or the person which acquires by conveyance or transfer or which leases all or
        substantially all of the properties and assets of the Company shall be a corporation, association or other legal entity organized and existing under the laws of the United States of America, any State thereof or the District of Columbia and
        expressly assumes the due and punctual payment of the principal of and any premium and interest on the Subordinated Notes according to their terms, and the due and punctual performance of all covenants and conditions hereof on the part of the
        Company to be performed or observed; and

       

      (ii)         immediately after giving effect to such transaction, no Event of Default, and no event which, after notice or lapse of time or both, would
        become an Event of Default, shall have happened and be continuing.

       

      “Change in Bank Control” means the sale, transfer, lease or conveyance by the Company, or an issuance of stock by the Bank, in either case resulting in ownership by the Company of less than 80% of the Bank.

       

      9.          [Reserved].

       

      10.        Denominations.  The Subordinated Notes are issuable only in registered form without interest coupons in minimum denominations of
        $250,000 and integral multiples of $1,000 in excess thereof.

       

      
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      11.        Charges and Transfer Taxes.  No service charge will be made for any registration of transfer or exchange of this Subordinated Note, or
        any redemption or repayment of this Subordinated Note, or any conversion or exchange of this Subordinated Note for other types of securities or property, but the Company may require payment of a sum sufficient to pay all taxes, assessments or other
        governmental charges that may be imposed in connection with the transfer or exchange of this Subordinated Note from the Noteholder requesting such transfer or exchange.

       

      12.        Payment Procedures.  Payment of the principal and interest payable on the Stated Maturity will be made by check, by wire transfer or by
        Automated Clearing House (ACH) transfer in immediately available funds to a bank account in the United States designated by the Noteholder if such Noteholder shall have previously provided wire instructions to the Company, upon presentation and
        surrender of this Subordinated Note at the Payment Office (as defined in Section 22 below) or at such other place or places as the Company shall designate by notice to the Noteholders as the Payment Office, provided that this Subordinated
        Note is presented to the Company in time for the Company to make such payments in such funds in accordance with its normal procedures.  Payments of interest (other than interest payable on the Stated Maturity) shall be made by wire transfer in
        immediately available funds or check mailed to the registered Noteholder, as such person’s address appears on the Security Register (as defined below).  Interest payable on any Interest Payment Date shall be payable to the Noteholder in whose name
        this Subordinated Note is registered at the close of business on the fifteenth calendar day prior to the applicable Interest Payment Date, without regard to whether such date is a Business Day, except that interest not paid on the Interest Payment
        Date, if any, will be paid to the Noteholder in whose name this Subordinated Note is registered at the close of business on a special record date fixed by the Company (a “Special Record Date”), notice of which shall be given to the
        Noteholder not less than 10 calendar days prior to such Special Record Date.  To the extent permitted by applicable law, interest shall accrue, at the rate at which interest accrues on the principal of this Subordinated Note, on any amount of
        principal or interest on this Subordinated Note not paid when due.  All payments on this Subordinated Note shall be applied first against interest due hereunder; and then against principal due hereunder.  The Noteholder acknowledges and agrees that
        the payment of all or any portion of the outstanding principal amount of this Subordinated Note and all interest hereon shall be pari passu in right of payment and in all other respects to the other
        Subordinated Notes.  In the event that the Noteholder receives payments in excess of its pro rata share of the Company’s payments to the Noteholders of all of the Subordinated Notes, then the Noteholder shall hold in trust all such excess payments
        for the benefit of the holders of the other Subordinated Notes and shall pay such amounts held in trust to such other Noteholders upon demand by such Noteholders.

       

      13.        Form of Payment.  Payments of principal and interest on this Subordinated Note shall be made in such coin or currency of the United
        States of America as at the time of payment shall be legal tender for the payment of public and private debts.

       

      
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      14.        Registration of Transfer, Security Register.  Except as otherwise provided herein, this Subordinated Note is transferable in whole or in
        part, and may be exchanged for a like aggregate principal amount of Subordinated Notes of other authorized denominations, by the Noteholder in person, or by its attorney duly authorized in writing, at the Payment Office.  The Company shall maintain
        a register providing for the registration of the Subordinated Notes and any exchange or transfer thereof (the “Security Register”).  Upon surrender or presentation of this Subordinated Note for exchange or registration of transfer, the
        Company shall execute and deliver in exchange therefor a Subordinated Note or Subordinated Notes of like aggregate principal amount, each in a minimum denomination of $250,000 or any amount in excess thereof which is an integral multiple of $1,000
        (and, in the absence of an opinion of counsel satisfactory to the Company to the contrary, bearing the restrictive legend(s) set forth hereinabove) and that is or are registered in such name or names requested by the Noteholder.  Any Subordinated
        Note presented or surrendered for registration of transfer or for exchange shall be duly endorsed and accompanied by a written instrument of transfer in such form as is attached hereto and incorporated herein, duly executed by the Noteholder or its
        attorney duly authorized in writing, with such tax identification number or other information for each person in whose name a Subordinated Note is to be issued, and accompanied by evidence of compliance with any restrictive legend(s) appearing on
        such Subordinated Note or Subordinated Notes as the Company may reasonably request to comply with applicable law.  No exchange or registration of transfer of this Subordinated Note shall be made on or after (i) the fifteenth (15th) day
        immediately preceding the Stated Maturity or (ii) the due delivery of notice of redemption.

       

      15.      Priority.  The Subordinated Notes rank pari passu among themselves and pari passu, in the event of any insolvency proceeding, dissolution, assignment for the benefit of creditors, reorganization, restructuring of debt, marshaling of assets and liabilities or similar proceeding or any liquidation or
        winding up of the Company with all other present or future unsecured subordinated debt obligations of the Company, except any unsecured subordinated debt that, pursuant to its express terms, is senior or subordinate in right of payment to the
        Subordinated Notes and all Senior Indebtedness.

       

      16.        Ownership.  Prior to due presentment of this Subordinated Note for registration of transfer, the Company may treat the Noteholder in
        whose name this Subordinated Note is registered in the Security Register as the absolute owner of this Subordinated Note for receiving payments of principal and interest on this Subordinated Note and for all other purposes whatsoever, whether or
        not this Subordinated Note be overdue, and the Company shall not be affected by any notice to the contrary.

       

      17.        Waiver and Consent.

       

      (a)         Any consent or waiver given by the holder of this Subordinated Note shall be conclusive and binding upon such Noteholder and upon all future
        holders of this Subordinated Note and of any Subordinated Note issued upon the registration of transfer hereof or in exchange therefor or in lieu hereof, whether or not notation of such consent or waiver is made upon this Subordinated Note.  This
        Subordinated Note may also be amended or waived pursuant to, and in accordance with, the provisions of Section 7.3 of the Purchase Agreement.  No delay or omission of the holder of this Subordinated Note to exercise any right or remedy accruing
        upon any Event of Default shall impair such right or remedy or constitute a waiver of any such Event of Default or an acquiescence therein. Any insured depository institution which shall be a holder of this Subordinated Note or which otherwise
        shall have any beneficial ownership interest in this Subordinated Note shall, by its acceptance of such Subordinated Note (or beneficial interest therein), be deemed to have waived any right of offset with respect to the repayment of the
        indebtedness evidenced thereby.

       

      
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      (b)         No waiver or amendment of any term, provision, condition, covenant or agreement in the Subordinated Notes shall be effective except with the
        consent of the Noteholders holding at least fifty percent (50%) in aggregate principal amount (excluding any Subordinated Notes held by the Company or any of its Affiliates) of the Subordinated Notes at the time outstanding; provided, however, that without the consent of each Noteholder of an affected Subordinated Note, no such amendment or waiver may:  (i) reduce the principal amount of any
        Subordinated Note; (ii) reduce the rate of or change the time for payment of interest on any Subordinated Note; (iii) extend the maturity of any Subordinated Note; (iv) change the currency in which payment of the obligations of the Company under
        the Subordinated Notes are to be made; (v) lower the percentage of aggregate principal amount of outstanding Subordinated Notes required to approve any amendment of the Subordinated Notes; (vi) make any changes to Section 5 (Events of
        Default; Acceleration); Section 6 (Failure to Make Payments); Section 7 (Affirmative Covenants of the Company); Section 8 (Negative Covenants of the Company) or Section 17 (Waiver and Consent) of the Subordinated
        Notes that adversely affects the rights of any Noteholder; or (vii) disproportionately affect any of the Noteholders of the then outstanding Subordinated Notes.  Notwithstanding the foregoing, the Company may amend or supplement the Subordinated
        Notes without the consent of the Noteholders to cure any ambiguity, defect or inconsistency or to provide for uncertificated Subordinated Notes in addition to or in place of certificated Subordinated Notes, or to make any change that does not
        adversely affect the rights of any Noteholder of any of the Subordinated Notes.  No failure to exercise or delay in exercising, by any Noteholder of the Subordinated Notes, of any right, power or privilege hereunder shall operate as a waiver
        thereof, nor shall any single or partial exercise of any right, power or privilege preclude any other or further exercise thereof, or the exercise of any other right or remedy provided by law, except as restricted hereby.  The rights and remedies
        provided in this Subordinated Note are cumulative and not exclusive of any right or remedy provided by law or equity.  No notice or demand on the Company in any case shall, in itself, entitle the Company to any other or further notice or demand in
        similar or other circumstances or constitute a waiver of the rights of the Noteholders to any other or further action in any circumstances without notice or demand.  No consent or waiver, expressed or implied, by the Noteholders to or of any breach
        or default by the Company in the performance of its obligations hereunder shall be deemed or construed to be a consent or waiver to or of any other breach or default in the performance of the same or any other obligations of the Company hereunder. 
        Failure on the part of the Noteholders to complain of any acts or failure to act or to declare an Event of Default, irrespective of how long such failure continues, shall not constitute a waiver by the Noteholders of their rights hereunder or
        impair any rights, powers or remedies on account of any breach or default by the Company.

       

      18.        Absolute and Unconditional Obligation of the Company.  No provisions of this Subordinated Note shall alter or impair the obligation of
        the Company, which is absolute and unconditional, to pay the principal and interest on this Subordinated Note at the times, places and rate, and in the coin or currency, herein prescribed.

       

      19.        Successors and Assigns.  This Subordinated Note shall be binding upon the Company and inure to the benefit of the Noteholder and its
        respective successors and permitted assigns.  The Noteholder may assign all, or any part of, or any interest in, the Noteholder’s rights and benefits hereunder.  To the extent of any such assignment, such assignee shall have the same rights and
        benefits against the Company and shall agree to be bound by and to comply with the terms and conditions of the Purchase Agreement as it would have had if it were the Noteholder hereunder.

       

      
        21

        
          


      

      20.          No Sinking Fund; Convertibility.  This Subordinated Note is not entitled to the benefit of any sinking fund.  This Subordinated Note is
        not convertible into or exchangeable for any of the equity securities, other securities or assets of the Company or any subsidiary.

       

      21.          No Recourse Against Others.  No recourse under or upon any obligation, covenant or agreement contained in this Subordinated Note, or
        for any claim based thereon or otherwise in respect thereof, will be had against any past, present or future shareholder, employee, officer, or director, as such, of the Company or of any predecessor or successor, either directly or through the
        Company or any predecessor or successor, under any rule of law, statute or constitutional provision or by the enforcement of any assessment or by any legal or equitable proceeding or otherwise, all such liability being expressly waived and released
        by the acceptance of this Subordinated Note by the holder of this Subordinated Note and as part of the consideration for the issuance of this Subordinated Note.

       

      22.       Notices.  All notices to the Company under this Subordinated Note shall be in writing and addressed to the Company at 302 Main Street,
        Catskill, NY 12414, Attention: Donald E. Gibson, or to such other address as the Company may provide to the Noteholders (the “Payment Office”).  All notices to the Noteholders shall be deemed to have been given if in writing and if delivered
        personally, or if mailed, postage prepaid, by United States registered or certified mail, return receipt requested, or if delivered by a responsible overnight commercial courier promising next business day delivery. Any notice given in accordance with the foregoing shall be deemed given when delivered personally or, if mailed, three (3) Business Days after it shall have been deposited in the United States mails as aforesaid or, if sent by
        overnight courier, the Business Day following the date of delivery to such courier (provided next business day delivery was requested).

       

      23.        Further Issues.  The Company may, without the consent of the Noteholders, create and issue additional notes having the same terms and
        conditions of the Subordinated Notes (except for the Issue Date) so that such further notes shall be consolidated and form a single series with the Subordinated Notes.

       

      24.        Governing Law; Interpretation.  THIS SUBORDINATED NOTE WILL BE DEEMED TO BE A CONTRACT MADE UNDER THE LAWS OF THE STATE OF NEW YORK AND
        WILL BE GOVERNED BY, AND CONSTRUED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF NEW YORK WITHOUT REGARD TO CONFLICT OF LAW PRINCIPLES THEREOF.

       

      
        22

        
          


      

      IN WITNESS WHEREOF, the undersigned has caused this Subordinated Note to be duly executed and attested.

       

      	 	
              

              

            	GREENE COUNTY BANCORP, INC.
	 	 	 	 
	 	
              By:

            	 
	 	 	
              Name:

            	
               Donald Gibson

            
	 	 	
              Title:

            	
               President and Chief Executive Officer

            


      

      

      	
              ATTEST:

            	 
	 	 
	
              Name:

            	
              Susan Timan

            	 
	
              Title:

            	
              Corporate Secretary

            	 


      

      

      [Signature Page to Subordinated Note]

      

      

      
        
          


      

      ASSIGNMENT FORM

       

      To assign this Subordinated Note, fill in the form below: (I) or (we) assign and transfer this Subordinated Note to:

      

        


      (Print or type assignee’s name, address and zip code)

      

        


      (Insert assignee’s social security or tax I.D. No.)

      

      

      and irrevocably appoint _______________________ agent to transfer this Subordinated Note on the books of the Company. The agent may substitute another to act for him.

      

      

      
        	 Date:	
                 

              	 	
                 Your signature:

              	 
	 	 	 	

              


      

      (Sign exactly as your name appears on the face of this Subordinated Note)

      

      

      
        	
                 

              	
                 Tax Identification No:

              	 


      

      

      

      
        	
                 Signature Guarantee: 

                

              	 


      

      (Signatures must be guaranteed by an eligible guarantor institution (banks, stockbrokers, savings and loan associations and credit unions with membership in an approved signature guarantee
        medallion program), pursuant to Rule 17Ad-15 promulgated under the Securities Exchange Act of 1934, as amended (the “Exchange Act”)).

      

      

      The undersigned certifies that it [is / is not] an Affiliate of the Company and that, to its knowledge, the proposed transferee [is / is not] an Affiliate of the Company.

      

      

      In connection with any transfer or exchange of this Subordinated Note occurring prior to the date that is one year after the later of the date of original issuance of this Subordinated Note and the
        last date, if any, on which this Subordinated Note was owned by the Company or any Affiliate of the Company, the undersigned confirms that this Subordinated Note is being:

      CHECK ONE BOX BELOW:

       

      
        
          	☐	(1)  

                	acquired for the undersigned’s own account, without transfer;


        

      

       

      
        
          	☐	(2)

                	transferred to the Company;


        

      

       

      
        
          	☐	(3) 

                	transferred in accordance and in compliance with Rule 144A under the Securities Act of 1933, as amended (the “Securities Act”);


        

      

       

      
        
          	☐	(4)

                	transferred under an effective registration statement under the Securities Act;


        

      

       

      
        
          	☐	(5)

                	transferred in accordance with and in compliance with Regulation S under the Securities Act;


        

      

       

      
        
          


      

      
        
          	☐	(6)

                	transferred to an institutional “accredited investor” (as defined in Rule 501(a)(1), (2), (3) or (7) under the Securities Act);


        

      

       

      
        
          	☐	(7)

                	transferred to an “accredited investor” (as defined in Rule 501(a)(4) under the Securities Act), not referred to in item (6) that has been provided with the information
                  designated under Section 4(d) of the Securities Act of 1933; or


        

      

       

      
        
          	☐	(7)

                	transferred in accordance with another available exemption from the registration requirements of the Securities Act.


        

      

       

      Unless one of the boxes is checked, the Company will refuse to register this Subordinated Note in the name of any person other than the registered holder thereof; provided, however, that if box (5), (6), (7) or (8)
        is checked, the Company may require, prior to registering any such transfer of this Subordinated Note, in its sole discretion, such legal opinions, certifications and other information as the Company may reasonably request to confirm that such
        transfer is being made pursuant to an exemption from, or in a transaction not subject to, the registration requirements of the Securities Act such as the exemption provided by Rule 144 under such Act.

       
        	
                 Signature:

              	
                 

              


      

         

      

      
        	
                 Signature Guarantee:

                

              	
                 

              


      

      (Signatures must be guaranteed by an eligible guarantor institution (banks, stockbrokers, savings and loan associations and credit unions with membership in an approved signature guarantee
        medallion program), pursuant to Exchange Act Rule 17Ad-l5).

       

      TO BE COMPLETED BY PURCHASER IF BOX (1) OR (3) ABOVE IS CHECKED.

      

      

      The undersigned represents and warrants that it is purchasing this Subordinated Note for its own account or an account with respect to which it exercises sole investment discretion and that it and
        any such account is a “qualified institutional buyer” within the meaning of Rule 144A under the Securities Act and is aware that the sale to it is being made in reliance on Rule 144A and acknowledges that it has received such information regarding
        the Company as the undersigned has requested pursuant to Rule 144A or has determined not to request such information and that it is aware that the transferor is relying upon the undersigned’s foregoing representations in order to claim the
        exemption from registration provided by Rule 144A.

      

      

      
        	
                 Date:

              	
                 

              	
                 

              	
                 Signature: