<PAGE>   1
                                                            EXHIBIT 10.16


                TAPPAN ZEE FINANCIAL, INC. 1996 STOCK OPTION PLAN
                           FOR OFFICERS AND EMPLOYEES
                        INCENTIVE STOCK OPTION AGREEMENT

                                                       -          -
-----------------------------------------       ------   --------  ------
            Name of Optionee                    Social   Security  Number


--------------------------------------------------------------------------------
                                 Street Address


--------------------------   --------------------   ----------------------------
          City                      State                 ZIP Code

This Incentive Stock Option Agreement is intended to set forth the terms and
conditions on which an Incentive Stock Option has been granted under the Tappan
Zee Financial, Inc. 1996 Stock Option Plan for Officers and Employees. Set forth
below are the specific terms and conditions applicable to this Incentive Stock
Option. Attached as Exhibit A are its general terms and conditions. The
Agreement set forth herein shall be effective as of July 11, 1996 and shall
amend and supersede, in its entirety, any other Incentive Stock Option Agreement
issued to the Optionee as of such date.

<TABLE>
<CAPTION>
=======================================================================================================================
             Option Grant                     (A)              (B)             (C)           (D)                (E)
=======================================================================================================================
        <S>                                  <C>              <C>             <C>           <C>                <C> 
                      Grant Date:
-----------------------------------------------------------------------------------------------------------------------
        Class of Optioned Shares*            Common           Common          Common        Common             Common
-----------------------------------------------------------------------------------------------------------------------
          No. of Optioned Shares*
-----------------------------------------------------------------------------------------------------------------------
        Exercise Price Per Share*
-----------------------------------------------------------------------------------------------------------------------
             VESTING
-----------------------------------------------------------------------------------------------------------------------
          Earliest Exercise Date*
-----------------------------------------------------------------------------------------------------------------------
          Option Expiration Date*
=======================================================================================================================
</TABLE>

*Subject to adjustment as provided in the Plan and the General Terms and
Conditions.

By signing where indicated below, Tappan Zee Financial, Inc. (the "Company")
grants this Incentive Stock Option upon the specified terms and conditions, and
the Optionee acknowledges receipt of this Incentive Stock Option Agreement,
including Exhibit A, and agrees to observe and be bound by the terms and
conditions set forth herein.

TAPPAN ZEE FINANCIAL, INC.                     OPTIONEE


By
  -------------------------------              ----------------------------
Name:
Title:

--------------------------------------------------------------------------------
INSTRUCTIONS: This page should be completed by or on behalf of the Compensation
Committee. Any blank space intentionally left blank should be crossed out. An
option grant consists of a number of optioned shares with uniform terms and
conditions. Where options are granted on the same date with varying terms and
conditions (for example, varying exercise prices or earliest exercise dates),
the options should be recorded as a series of grants each with its own uniform
terms and conditions.


<PAGE>   2



                                                                       EXHIBIT A
  TAPPAN ZEE FINANCIAL, INC. 1996 STOCK OPTION PLAN FOR OFFICERS AND EMPLOYEES
                        INCENTIVE STOCK OPTION AGREEMENT

                          GENERAL TERMS AND CONDITIONS


         SECTION 1.      INCENTIVE STOCK OPTION. The Company intends the Option
evidenced hereby to be an "incentive stock option" within the meaning of section
422 of the Internal Revenue Code of 1986.

         SECTION 2.      OPTION PERIOD. (a) Subject to section 2(b), the 
Optionee shall have the right to purchase all or any portion of the optioned
Common Stock at any time during the period ("Option Period") commencing on the
Earliest Exercise Date and ending on the earliest to occur of the following
dates:

                  (i)  removal for cause in accordance with the Company's 
bylaws; or

                  (ii) the last day of the ten-year period commencing on the
         date on which the Option was granted.

         (b)   Upon the termination of the Optionee's Service with the Company,
any Option granted hereunder whose Earliest Exercise Date has not occurred is
deemed forfeited. For this purpose, an Optionee's Service shall be deemed to
continue for so long as the Optionee is serving as an officer, employee, outside
director, advisory director, emeritus director or consultant to the Company or
is subject to and is observing the terms of a written agreement restricting his
ability to compete or imposing other restrictive covenants. In the event of the
Optionee's death or disability (as defined in the Plan) while in Service, the
date of death or disability shall be the Earliest Exercise Date of any Options
that are not currently exercisable. To the extent authorized pursuant to a Plan
provision that is approved by the Company's shareholders after October 5, 1996,
in the event of the Optionee's retirement (as defined in the Plan) or a change
of control (as defined in the Plan), the date of such retirement or change of
control shall be the Earliest Exercise Date of any Options that are not already
exercisable.

         SECTION 3.      EXERCISE PRICE. During the Option Period, and after the
applicable Earliest Exercise Date, the Optionee shall have the right to purchase
all or any portion of the Optioned Common Stock at the Exercise Price per Share.

         SECTION 4.      METHOD OF EXERCISE. The Optionee may, at any time 
during the Option Period provided by section 2, exercise his right to purchase
all or any part of the optioned Common Stock then available for purchase;
provided, however, that the minimum number of shares of optioned Common Stock
which may be purchased shall be one hundred (100) or, if less, the total number
of shares of optioned Common Stock then available for pur chase. The Optionee
shall exercise such right by:

         (a)   giving written notice to the Committee, in the form attached 
hereto as Appendix A; and

         (b)   delivering to the Committee full payment of the Exercise Price 
for the Optioned Shares to be purchased.

The date of exercise shall be the earliest date practicable following the date
the requirements of this section 4 have been satisfied, but in no event more
than three (3) days after such date. Payment shall be made (i) in United States
dollars by certified check, money order or bank draft made payable to the order
of Tappan Zee Financial, Inc., (ii) in Shares duly endorsed for transfer and
with all necessary stock transfer tax stamps attached, already owned by the
Optionee and having a fair market value equal to the Exercise Price, such fair
market value to be determined in such manner as may be provided by the Committee
or as may be required in order to comply with or conform to the requirements of
any applicable laws or regulations, or (iii) in a combination of (i) and (ii).

         SECTION 5.      DELIVERY AND REGISTRATION OF OPTIONED SHARES. As soon 
as is practicable following the date on which the Optionee has satisfied the
requirements of section 4, the Committee shall take such action as is necessary
to cause the Company to issue a stock certificate evidencing the Optionee's
ownership of the optioned Common Stock that has been purchased. The Optionee
shall have no right to vote or to receive dividends, nor have

                                       -2-

<PAGE>   3



any other rights with respect to optioned Common Stock, prior to the date as of
which such optioned Common Stock is transferred to the Optionee on the stock
transfer records of the Company, and no adjustments shall be made for any
dividends or other rights for which the record date is prior to the date as of
which such transfer is effected. The obligation of the Company to deliver Common
Stock under this Agreement shall, if the Committee so requests, be conditioned
upon the receipt of a representation as to the investment intention of the
person to whom such Common Stock is to be delivered, in such form as the
Committee shall determine to be necessary or advisable to comply with the
provisions of applicable federal, state or local law. It may be provided that
any such representation shall become inoperative upon a registration of the
Common Stock or upon the occurrence of any other event eliminating the necessity
of such representation. The Company shall not be required to deliver any Common
Stock under this Agreement prior to (a) the admission of such Common Stock to
listing on any stock exchange on which Common Stock may then be listed, or (b)
the completion of such registration or other qualification under any state or
federal law, rule or regulations as the Committee shall determine to be
necessary or advisable.

         SECTION 6.      ADJUSTMENTS IN THE EVENT OF REORGANIZATION. In the 
event of any merger, consolidation, or other business reorganization in which
the Company is the surviving entity, and in the event of any stock split, stock
dividend or other event generally affecting the number of shares of Common Stock
held by each per son who is then a shareholder of record, the number of shares
of Common Stock subject to the option granted hereunder and the Exercise Price
per share of such option shall be adjusted in accordance with section 5.3 of the
Plan to account for such event. In the event of any merger, consolidation, or
other business reorganization in which the Company is not the surviving entity,
the option granted hereunder shall be cancelled or adjusted in accordance with
the Plan. In the event that the Company shall declare and pay any dividend with
respect to Shares (other than a dividend payable in Shares or a regular
quarterly cash dividend), including a dividend which results in a nontaxable
return of capital to the holders of Shares for federal income tax purposes, or
otherwise than by dividend makes distribution of property to the holders of its
Shares, the Company shall, in the discretion of the Committee, (a) make an
equivalent payment to each Person holding an outstanding Option as of the record
date for such dividend in accordance with section 5.3(c)(i) of the Plan or (b)
adjust the Exercise Price per Share of outstanding Options in such a manner as
the Committee may determine to be appropriate to equitably reflect the payment
of the dividend or (c) take the action described in this section 6(a) with
respect to certain outstanding Options and the action described in section 6(b)
with respect to the remaining outstanding Options provided, however, that no
such action shall be taken without the approval of the Office of Thrift
Supervision until the stockholders of the Company have voted to approve the
provisions of section 5.3(c) of the Plan in a vote taken after October 5, 1996.

         SECTION 7.      NO RIGHT TO CONTINUED SERVICE. Nothing in this 
Agreement nor any action of the Board or Committee with respect to this
Agreement shall be held or construed to confer upon the Optionee any right to a
continuation of service by the Company. The Optionee may be dismissed or
otherwise dealt with as though this Agreement had not been entered into.

         SECTION 8.      TAXES. Where any person is entitled to receive shares
pursuant to the exercise of the Option granted hereunder, the Company shall have
the right to require such person to pay to the Company the amount of any tax
which the Company is required to withhold with respect to such shares, or, in
lieu thereof, to retain, or to sell without notice, a sufficient number of
shares to cover the amount required to be withheld.

         SECTION 9.      NOTICES. Any communication required or permitted to be 
given under the Plan, including any notice, direction, designation, comment,
instruction, objection or waiver, shall be in writing and shall be deemed to
have been given at such time as it is delivered personally or five (5) days
after mailing if mailed, postage prepaid, by registered or certified mail,
return receipt requested, addressed to such party at the address listed below,
or at such other address as one such party may by written notice specify to the
other party:

         (a)            If to the Committee:

                        Tappan Zee Financial, Inc.
                        75 Broadway
                        Tarrytown, New York  10591

                        Attention:   Compensation Committee


                                       -3-

<PAGE>   4



         (b)   If to the Optionee, to the Optionee's address as shown in the
Company's personnel records.

         SECTION 10.     RESTRICTIONS ON TRANSFER. The option granted hereunder
shall not be subject in any manner to anticipation, alienation or assignment,
nor shall such option be liable for or subject to debts, contracts, liabilities,
engagements or torts, nor shall it be transferable by the Optionee other than by
will or by the laws of descent and distribution or as otherwise permitted by the
Plan.

         SECTION 11.     SUCCESSORS AND ASSIGNS. This Agreement shall inure to 
the benefit of and shall be binding upon the Company and the Optionee and their
respective heirs, successors and assigns.

         SECTION 12.     CONSTRUCTION OF LANGUAGE. Whenever appropriate in the
Agreement, words used in the singular may be read in the plural, words used in
the plural may be read in the singular, and words importing the masculine gender
may be read as referring equally to the feminine or the neuter. Any reference to
a section shall be a reference to a section of this Agreement, unless the
context clearly indicates otherwise. Capitalized terms not specifically defined
herein shall have the meanings assigned to them under the Plan.

         SECTION 13.     GOVERNING LAW. This Agreement shall be construed,
administered and enforced according to the laws of the State of New York without
giving effect to the conflict of laws principles thereof, except to the extent
that such laws are preempted by the federal law.

         SECTION 14.     AMENDMENT. This Agreement may be amended, in whole or 
in part and in any manner not inconsistent with the provisions of the Plan, at
any time and from time to time, by written agreement between the Company and the
Optionee.

         SECTION 15.     PLAN PROVISIONS CONTROL. This Agreement and the rights 
and obligations created hereunder shall be subject to all of the terms and
conditions of the Plan. In the event of any conflict between the provisions of
the Plan and the provisions of this Agreement, the terms of the Plan, which are
incorporated herein by reference, shall control. By signing this Agreement, the
Optionee acknowledges receipt of a copy of the Plan.

         SECTION 16.     CHANGE IN CONTROL. A "change in control" shall be as
defined in the Plan.

                                       -4-

<PAGE>   5



                 APPENDIX A TO INCENTIVE STOCK OPTION AGREEMENT
  Tappan Zee Financial, Inc. 1996 Stock Option Plan for Officers and Employees
                  NOTICE OF EXERCISE OF INCENTIVE STOCK OPTION

1.       INSTRUCTIONS. Use this Notice to inform the Committee administering the
         Tappan Zee Financial, Inc. 1996 Stock Option Plan for Officers and
         Employees ("Plan") that you are exercising your right to purchase
         shares of common stock ("Shares") of Tappan Zee Financial, Inc.
         ("Tappan Zee") pursuant to a non-qualified stock option ("Option")
         granted under the Plan. If you are not the person to whom the Option
         was granted ("Option Recipient"), you must attach to this Notice proof
         of your right to exercise the Option granted under the Incentive Stock
         Option Agreement entered into between Tappan Zee and the Option
         Recipient ("Agreement"). This Notice should be personally delivered or
         mailed by certified mail, return receipt requested to: Tappan Zee
         Financial, Inc., 75 Broadway, Tarrytown, New York 10591, Attention:
         Compensation Committee. The effective date of the exercise of the
         Option shall be the earliest date practicable following the date this
         Notice is received by the Committee, but in no event more than three
         days after such date ("Effective Date"). Except as specifically
         provided to the contrary herein, capitalized terms shall have the
         meanings assigned to them under the Plan. This Notice is subject to all
         of the terms and conditions of the Plan and the Agreement.


2.       PURCHASE OF SHARES. Pursuant to the Agreement made and entered into as
         of _____________________, 19 ___ [enter date of Agreement] by and
         between Tappan Zee and [enter the name of the Option Recipient], I
         hereby exercise my right to purchase __________ Shares at an Exercise
         Price per Share of $_________, for a Total Exercise Price of
         $_____________ [enter the product of the number of Shares multiplied by
         the Exercise Price per Share]. As a payment for such Shares, I [check
         and complete one or more; the sum of the amounts shown in (a), (b) and
         (c), must equal the Total Exercise Price shown above:
<TABLE>
         <S>     <C>    <C>                                                      <C>
         (A)     [ ]    enclose a certified check, money order, or bank draft    $__________
                        payable to the order of Tappan Zee Financial, Inc. in 
                        the amount of                                        
         (B)     [ ]    enclose Shares duly endorsed for transfer to Tappan Zee  $__________
                        with all necessary stock transfer stamps attached and 
                        having a fair market value of
                                       
                        Total Exercise Price                                     $__________
</TABLE>

3.       ISSUANCE OF CERTIFICATES. I hereby direct that the stock certificates
         representing the Shares purchased pursuant to section 2 above be issued
         to the following person(s) in the amount specified below:
<TABLE>
<CAPTION>

                 Name and Address              Social Security No.             No of Shares
                 ----------------              -------------------             ------------
<S>                                            <C>                           <C>
-------------------------------------------          -      -
-------------------------------------------    ------ ------ --------        ---------------
-------------------------------------------          -      -
-------------------------------------------    ------ ------ --------        ---------------
</TABLE>

4.       WITHHOLDING ELECTIONS. [For Employee Option Recipients only.
         Beneficiaries and Outside Directors should not complete.] I understand
         that I am responsible for the amount of federal, state and local taxes
         required to be withheld with respect to the Shares to be issued to me
         pursuant to this Notice, but that I may request Tappan Zee to retain or
         sell a sufficient number of such Shares to cover the amount to be
         withheld. I hereby request that any taxes required to be withheld be
         paid in the following manner [check one]:


         (A)      [ ]      With a certified or bank check that I will deliver 
                           to the Administrator on the day after the Effective 
                           Date of my Option exercise.

         (B)      [ ]      With the proceeds from a sale of Shares that would 
                           otherwise be distributed to me.

        I understand that the withholding elections I have made on this form are
        not binding on the Committee, and that the Committee will decide the
        amount to be withheld and the method of withholding and advise me of its
        decision prior to the Effective Date. I further understand that the
        Committee may request additional information or assurances regarding the
        manner and time at which I will report the income attributable to the
        distribution to be made to me.

        I further understand that if I have elected to have Shares sold to
        satisfy tax withholding, I may be asked to pay a minimal amount of such
        taxes in cash in order to avoid the sale of more Shares than are
        necessary.

5.      COMPLIANCE WITH TAX AND SECURITIES LAWS. I understand that I must rely
        on, and consult with, my own tax and legal counsel (and not Tappan Zee
        Financial, Inc.) regarding the application of all laws -- particularly
        tax and securities laws -- to the transactions to be effected pursuant
        to my Option and this Notice. I understand that I will be responsible
        for paying any federal, state and local taxes that may become due upon
        the sale (including a sale pursuant to a "cashless exercise") or other
        disposition of Shares issued pursuant to this Notice and that I must
        consult with my own tax advisor regarding how and when such income will
        be reportable.


----------------------------------                    -------------------------
             Signature                                           Date

--------------------------------------------------------------------------------
                                     Address
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
COMPENSATION COMMITTEE
Received  [check one]: [ ] By Hand   [ ] By Mail Post Marked
                                                             ------------------
                                                              Date of Post Mark

By
   ----------------------------------------                  ------------------
             Authorized Signature                             Date of Receipt


<PAGE>   6
     TAPPAN ZEE FINANCIAL, INC. 1996 STOCK OPTION PLAN FOR OUTSIDE DIRECTORS
                      NON-QUALIFIED STOCK OPTION AGREEMENT
                                                       -          -
-----------------------------------------       ------   --------   ------
            Name of Optionee                    Social   Security  Number


--------------------------------------------------------------------------------
                                 Street Address


--------------------------   --------------------   ----------------------------
          City                      State                 ZIP Code

This Non-Qualified Stock Option Agreement is intended to set forth the terms and
conditions on which a Non-Qualified Stock Option has been granted under the
Tappan Zee Financial, Inc. 1996 Stock Option Plan for Outside Directors. Set
forth below are the specific terms and conditions applicable to this
Non-Qualified Stock Option. Attached as Exhibit A are its general terms and
conditions. The Agreement set forth herein shall be effective as of July 11,
1996 and shall amend and supersede, in its entirety, any other Non-Qualified
Stock Option Agreement issued to the Optionee as of such date.

<TABLE>
<CAPTION>
========================================================================================================================
          Option Grant                 (A)               (B)               (C)               (D)                (E)
========================================================================================================================
       <S>                            <C>              <C>                <C>               <C>               <C> 
                     Grant Date:
------------------------------------------------------------------------------------------------------------------------
       Class of Optioned Shares*      Common           Common             Common            Common            Common
------------------------------------------------------------------------------------------------------------------------
         No. of Optioned Shares*
------------------------------------------------------------------------------------------------------------------------
       Exercise Price Per Share*
------------------------------------------------------------------------------------------------------------------------
             VESTING
------------------------------------------------------------------------------------------------------------------------
         Earliest Exercise Date*
------------------------------------------------------------------------------------------------------------------------
         Option Expiration Date*
========================================================================================================================
</TABLE>
*Subject to adjustment as provided in the Plan and the General Terms and
Conditions.

By signing where indicated below, Tappan Zee Financial, Inc. (the "Company")
grants this Non-Qualified Stock Option upon the specified terms and conditions,
and the Optionee acknowledges receipt of this Non-Qualified Stock Option
Agreement, including Exhibit A, and agrees to observe and be bound by the terms
and conditions set forth herein.

TAPPAN ZEE FINANCIAL, INC.                     OPTIONEE


By
  -------------------------------              ----------------------------
Name:
Title:

--------------------------------------------------------------------------------
INSTRUCTIONS: This page should be completed by or on behalf of the Compensation
Committee. Any blank space intentionally left blank should be crossed out. An
option grant consists of a number of optioned shares with uniform terms and
conditions. Where options are granted on the same date with varying terms and
conditions (for example, varying exercise prices or earliest exercise dates),
the options should be recorded as a series of grants each with its own uniform
terms and conditions.


<PAGE>   7



                                                                       EXHIBIT A
     TAPPAN ZEE FINANCIAL, INC. 1996 STOCK OPTION PLAN FOR OUTSIDE DIRECTORS
                      NON-QUALIFIED STOCK OPTION AGREEMENT

                          GENERAL TERMS AND CONDITIONS


         SECTION 1.      NON-QUALIFIED STOCK OPTION. The Company intends the 
Option evidenced hereby not to be an "incentive stock option" within the meaning
of section 422 of the Internal Revenue Code of 1986.

         SECTION 2.      OPTION PERIOD. (a) Subject to section 2(b), the 
Optionee shall have the right to purchase all or any portion of the optioned
Common Stock at any time during the period ("Option Period") commencing on the
Earliest Exercise Date and ending on the earliest to occur of the following
dates:

                  (i)  removal for cause in accordance with the Company's 
bylaws; or

                  (ii) the last day of the ten-year period commencing on the
         date on which the Option was granted.

         (b)      Upon the termination of the Optionee's Service with the 
Company, any Option granted hereunder whose Earliest Exercise Date has not
occurred is deemed forfeited. For this purpose, an Optionee's Service shall be
deemed to continue for so long as the Optionee is serving as an officer,
employee, outside director, advisory director, emeritus director or consultant
to the Company or is subject to and is observing the terms of a written
agreement restricting his ability to compete or imposing other restrictive
covenants. In the event of the Optionee's death or disability (as defined in
the Plan) while in Service, the date of death or disability shall be the
Earliest Exercise Date of any Options that are not currently exercisable. To
the extent authorized pursuant to a Plan provision that is approved by the
Company's shareholders after October 5, 1996, in the event of the Optionee's
retirement (as defined in the Plan) or a change of control (as defined in the
Plan), the date of such retirement or change of control shall be the Earliest
Exercise Date of any Options that are not already exercisable.

         SECTION 3.      EXERCISE PRICE. During the Option Period, and after the
applicable Earliest Exercise Date, the Optionee shall have the right to purchase
all or any portion of the Optioned Common Stock at the Exercise Price per Share.

         SECTION 4.      METHOD OF EXERCISE. The Optionee may, at any time 
during the Option Period provided by section 2, exercise his right to purchase
all or any part of the optioned Common Stock then available for purchase;
provided, however, that the minimum number of shares of optioned Common Stock
which may be purchased shall be one hundred (100) or, if less, the total number
of shares of optioned Common Stock then available for pur chase. The Optionee
shall exercise such right by:

         (a)      giving written notice to the Committee, in the form
         attached hereto as Appendix A; and

         (b)      delivering to the Committee full payment of the Exercise
         Price for the Optioned Shares to be purchased.

The date of exercise shall be the earliest date practicable following the date
the requirements of this section 4 have been satisfied, but in no event more
than three (3) days after such date. Payment shall be made (i) in United States
dollars by certified check, money order or bank draft made payable to the order
of Tappan Zee Financial, Inc., (ii) in Shares duly endorsed for transfer and
with all necessary stock transfer tax stamps attached, already owned by the
Optionee and having a fair market value equal to the Exercise Price, such fair
market value to be determined in such manner as may be provided by the Committee
or as may be required in order to comply with or conform to the requirements of
any applicable laws or regulations, or (iii) in a combination of (i) and (ii).

         SECTION 5.      DELIVERY AND REGISTRATION OF OPTIONED SHARES. As soon 
as is practicable following the date on which the Optionee has satisfied the
requirements of section 4, the Committee shall take such action as is necessary
to cause the Company to issue a stock certificate evidencing the Optionee's
ownership of the optioned Common Stock that has been purchased. The Optionee
shall have no right to vote or to receive dividends, nor have

                                       -2-

<PAGE>   8



any other rights with respect to optioned Common Stock, prior to the date as of
which such optioned Common Stock is transferred to the Optionee on the stock
transfer records of the Company, and no adjustments shall be made for any
dividends or other rights for which the record date is prior to the date as of
which such transfer is effected. The obligation of the Company to deliver Common
Stock under this Agreement shall, if the Committee so requests, be conditioned
upon the receipt of a representation as to the investment intention of the
person to whom such Common Stock is to be delivered, in such form as the
Committee shall determine to be necessary or advisable to comply with the
provisions of applicable federal, state or local law. It may be provided that
any such representation shall become inoperative upon a registration of the
Common Stock or upon the occurrence of any other event eliminating the necessity
of such representation. The Company shall not be required to deliver any Common
Stock under this Agreement prior to (a) the admission of such Common Stock to
listing on any stock exchange on which Common Stock may then be listed, or (b)
the completion of such registration or other qualification under any state or
federal law, rule or regulations as the Committee shall determine to be
necessary or advisable.

         SECTION 6.      ADJUSTMENTS IN THE EVENT OF REORGANIZATION. In the 
event of any merger, consolidation, or other business reorganization in which
the Company is the surviving entity, and in the event of any stock split, stock
dividend or other event generally affecting the number of shares of Common Stock
held by each per son who is then a shareholder of record, the number of shares
of Common Stock subject to the option granted hereunder and the Exercise Price
per share of such option shall be adjusted in accordance with section 5.3 of the
Plan to account for such event. In the event of any merger, consolidation, or
other business reorganization in which the Company is not the surviving entity,
the option granted hereunder shall be cancelled or adjusted in accordance with
the Plan. In the event that the Company shall declare and pay any dividend with
respect to Shares (other than a dividend payable in Shares or a regular
quarterly cash dividend), including a dividend which results in a nontaxable
return of capital to the holders of Shares for federal income tax purposes, or
otherwise than by dividend makes distribution of property to the holders of its
Shares, the Company shall, in the discretion of the Committee, (a) make an
equivalent payment to each Person holding an outstanding Option as of the record
date for such dividend in accordance with section 5.3(c)(i) of the Plan or (b)
adjust the Exercise Price per Share of outstanding Options in such a manner as
the Committee may determine to be appropriate to equitably reflect the payment
of the dividend or (c) take the action described in this section 6(a) with
respect to certain outstanding Options and the action described in section 6(b)
with respect to the remaining outstanding Options provided, however, that no
such action shall be taken without the approval of the Office of Thrift
Supervision until the stockholders of the Company have voted to approve the
provisions of section 5.3(c) of the Plan in a vote taken after October 5, 1996.

         SECTION 7.      NO RIGHT TO CONTINUED SERVICE. Nothing in this 
Agreement nor any action of the Board or Committee with respect to this
Agreement shall be held or construed to confer upon the Optionee any right to a
continuation of service by the Company. The Optionee may be dismissed or
otherwise dealt with as though this Agreement had not been entered into.

         SECTION 8.      TAXES. Where any person is entitled to receive shares
pursuant to the exercise of the Option granted hereunder, the Company shall have
the right to require such person to pay to the Company the amount of any tax
which the Company is required to withhold with respect to such shares, or, in
lieu thereof, to retain, or to sell without notice, a sufficient number of
shares to cover the amount required to be withheld.

         SECTION 9.      NOTICES. Any communication required or permitted to be 
given under the Plan, including any notice, direction, designation, comment,
instruction, objection or waiver, shall be in writing and shall be deemed to
have been given at such time as it is delivered personally or five (5) days
after mailing if mailed, postage prepaid, by registered or certified mail,
return receipt requested, addressed to such party at the address listed below,
or at such other address as one such party may by written notice specify to the
other party:

         (a)   If to the Committee:
   
               Tappan Zee Financial, Inc.
               75 Broadway
               Tarrytown, New York  10591
   
               Attention:       Compensation Committee
   
   
                                -3-

<PAGE>   9



         (b)   If to the Optionee, to the Optionee's address as shown in the
Company's personnel records.

         SECTION 10.     RESTRICTIONS ON TRANSFER. The option granted hereunder
shall not be subject in any manner to anticipation, alienation or assignment,
nor shall such option be liable for or subject to debts, contracts, liabilities,
engagements or torts, nor shall it be transferable by the Optionee other than by
will or by the laws of descent and distribution or as otherwise permitted by the
Plan.

         SECTION 11.     SUCCESSORS AND ASSIGNS. This Agreement shall inure to 
the benefit of and shall be binding upon the Company and the Optionee and their
respective heirs, successors and assigns.

         SECTION 12.     CONSTRUCTION OF LANGUAGE. Whenever appropriate in the
Agreement, words used in the singular may be read in the plural, words used in
the plural may be read in the singular, and words importing the masculine gender
may be read as referring equally to the feminine or the neuter. Any reference to
a section shall be a reference to a section of this Agreement, unless the
context clearly indicates otherwise. Capitalized terms not specifically defined
herein shall have the meanings assigned to them under the Plan.

         SECTION 13.     GOVERNING LAW. This Agreement shall be construed,
administered and enforced according to the laws of the State of New York without
giving effect to the conflict of laws principles thereof, except to the extent
that such laws are preempted by the federal law.

         SECTION 14.     AMENDMENT. This Agreement may be amended, in whole or 
in part and in any manner not inconsistent with the provisions of the Plan,
at any time and from time to time, by written agreement between the Company and
the Optionee.

         SECTION 15.     PLAN PROVISIONS CONTROL. This Agreement and the rights 
and obligations created hereunder shall be subject to all of the terms and
conditions of the Plan. In the event of any conflict between the provisions of
the Plan and the provisions of this Agreement, the terms of the Plan, which are
incorporated herein by reference, shall control. By signing this Agreement, the
Optionee acknowledges receipt of a copy of the Plan.

         SECTION 16.     CHANGE IN CONTROL. A "change in control" shall be as
defined in the Plan.

                                       -4-

<PAGE>   10



               APPENDIX A TO NON-QUALIFIED STOCK OPTION AGREEMENT
     Tappan Zee Financial, Inc. 1996 Stock Option Plan for Outside Directors
                NOTICE OF EXERCISE OF NON-QUALIFIED STOCK OPTION

1.       INSTRUCTIONS. Use this Notice to inform the Committee administering the
         Tappan Zee Financial, Inc. 1996 Stock Option Plan for Outside Directors
         ("Plan") that you are exercising your right to purchase shares of
         common stock ("Shares") of Tappan Zee Financial, Inc. ("Tappan Zee")
         pursuant to a non-qualified stock option ("Option") granted under the
         Plan. If you are not the person to whom the Option was granted ("Option
         Recipient"), you must attach to this Notice proof of your right to
         exercise the Option granted under the Non-Qualified Stock Option
         Agreement entered into between Tappan Zee and the Option Recipient
         ("Agreement"). This Notice should be personally delivered or mailed by
         certified mail, return receipt requested to: Tappan Zee Financial,
         Inc., 75 Broadway, Tarrytown, New York 10591, Attention: Compensation
         Committee. The effective date of the exercise of the Option shall be
         the earliest date practicable following the date this Notice is
         received by the Committee, but in no event more than three days after
         such date ("Effective Date"). Except as specifically provided to the
         contrary herein, capitalized terms shall have the meanings assigned to
         them under the Plan. This Notice is subject to all of the terms and
         conditions of the Plan and the Agreement.

2.       PURCHASE OF SHARES. Pursuant to the Agreement made and entered into as
         of _____________________, 19 ___ [enter date of Agreement] by and
         between Tappan Zee and [enter the name of the Option Recipient], I
         hereby exercise my right to purchase __________ Shares at an Exercise
         Price per Share of $_________, for a Total Exercise Price of
         $_____________ [enter the product of the number of Shares multiplied by
         the Exercise Price per Share]. As a payment for such Shares, I [check
         and complete one or more; the sum of the amounts shown in (a), (b) and
         (c), must equal the Total Exercise Price shown above:

<TABLE>
         <S>     <C>    <C>                                                      <C>
         (A)     [ ]    enclose a certified check, money order, or bank draft    $__________
                        payable to the order of Tappan Zee Financial, Inc. in 
                        the amount of                                        
         (B)     [ ]    enclose Shares duly endorsed for transfer to Tappan Zee  $__________
                        with all necessary stock transfer stamps attached and 
                        having a fair market value of
                                       
                        Total Exercise Price                                     $__________
</TABLE>

3.       ISSUANCE OF CERTIFICATES. I hereby direct that the stock certificates
         representing the Shares purchased pursuant to section 2 above be issued
         to the following person(s) in the amount specified below:
<TABLE>
<CAPTION>

                 Name and Address              Social Security No.             No of Shares
                 ----------------              -------------------             ------------
<S>                                            <C>                           <C>
-------------------------------------------          -      -
-------------------------------------------    ------ ------ --------        ---------------
-------------------------------------------          -      -
-------------------------------------------    ------ ------ --------        ---------------
</TABLE>

4.       WITHHOLDING ELECTIONS. [For Employee Option Recipients only.
         Beneficiaries and Outside Directors should not complete.] I understand
         that I am responsible for the amount of federal, state and local taxes
         required to be withheld with respect to the Shares to be issued to me
         pursuant to this Notice, but that I may request Tappan Zee to retain or
         sell a sufficient number of such Shares to cover the amount to be
         withheld. I hereby request that any taxes required to be withheld be
         paid in the following manner [check one]:


         (A)      [ ]      With a certified or bank check that I will deliver 
                           to the Administrator on the day after the Effective 
                           Date of my Option exercise.

         (B)      [ ]      With the proceeds from a sale of Shares that would 
                           otherwise be distributed to me.

     I understand that the withholding elections I have made on this form are
     not binding on the Committee, and that the Committee will decide the amount
     to be withheld and the method of withholding and advise me of its decision
     prior to the Effective Date. I further understand that the Committee may
     request additional information or assurances regarding the manner and time
     at which I will report the income attributable to the distribution to be
     made to me.

     I further understand that if I have elected to have Shares sold to satisfy
     tax withholding, I may be asked to pay a minimal amount of such taxes in
     cash in order to avoid the sale of more Shares than are necessary.

5.   COMPLIANCE WITH TAX AND SECURITIES LAWS. I understand that I must rely on,
     and consult with, my own tax and legal counsel (and not Tappan Zee
     Financial, Inc.) regarding the application of all laws -- particularly tax
     and securities laws -- to the transactions to be effected pursuant to my
     Option and this Notice. I understand that I will be responsible for paying
     any federal, state and local taxes that may become due upon the sale
     (including a sale pursuant to a "cashless exercise") or other disposition
     of Shares issued pursuant to this Notice and that I must consult with my
     own tax advisor regarding how and when such income will be reportable.



----------------------------------                    -------------------------
             Signature                                           Date

-------------------------------------------------------------------------------
                                     Address
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
COMPENSATION COMMITTEE
Received  [check one]: [ ] By Hand   [ ] By Mail Post Marked
                                                             ------------------
                                                              Date of Post Mark

By
   ----------------------------------------                  ------------------
             Authorized Signature                             Date of Receipt