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                                                                   Exhibit 10.31

                              EMPLOYMENT AGREEMENT
                              --------------------


     EMPLOYMENT AGREEMENT dated as of December 2, 1996 between THE DIME SAVINGS
BANK OF NEW YORK, FSB (the "Bank"), a federal stock savings bank having its
principal executive offices at 589 Fifth Avenue, New York, New York 10017, and
FRED B. KOONS (the "Executive").

                                  ___________

     A.  The Bank is desirous of employing the Executive upon the terms and
conditions set forth in this Agreement.

     B.  The Executive is desirous of being employed by the Bank upon the terms
and conditions set forth in this Agreement.
                                  ____________

     Therefore, the Bank and the Executive, intending to be legally bound, agree
as follows:

          1.  Employment.  Subject to the terms and conditions of this
              ----------
Agreement, the Bank hereby employs the Executive, and the Executive hereby
accepts such employment.

          2.  Term of Employment.  (a) The term of the Executive's employment
              ------------------
under this Agreement shall be deemed to have commenced on the date of this
Agreement and shall continue until the fifth anniversary of the date hereof
unless this Agreement has been terminated prior thereto in accordance with its
provisions.  (As used in this Agreement, (i) "Term" shall mean the full five-
year term of this Agreement and (ii) "remaining Term" shall mean the balance of
the Term remaining at a specified time.)
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          (b)  The Executive's employment may be terminated during the Term of
this Agreement by the Bank or the Executive in the manner specified in this
Agreement.  Any such termination of employment shall result in a termination of
this Agreement on the Effective Date of Termination (as defined in Section 13);
provided that, notwithstanding anything to the contrary in the foregoing, any
right of the Executive to any payments or benefits as a result of a termination
of the Executive's employment (as provided in this Agreement) shall survive the
termination of this Agreement.

          3.  Offices.  During the first three years of the Term, the Executive
              -------
shall serve as an officer of the Bank and its parent corporation, Dime Bancorp,
Inc. (the "Company").  In addition, during the first three years of the Term,
the Executive shall serve as an officer of the Bank's mortgage banking
subsidiary, Dime Mortgage, Inc. (the "Subsidiary").  During the fourth and fifth
years of the Term, the Executive shall serve as an executive employee of the
Bank. During the Term, the Executive shall also serve, for any period for which
the Executive may from time to time be elected, as an officer or director of
subsidiaries or affiliates of the Bank.

          4.  Duties.  (a) During the first two years of the Term, the Executive
              ------
shall serve as an Executive Vice President of the Bank and the Company and as
the Chief Executive Officer of the Subsidiary and shall perform such duties in
connection therewith as may be assigned to him from time to time by the Chief
Executive Officer of the Bank or the Company, as the case may be.

          (b)  During the third year of the Term, the Executive shall continue
to serve as an Executive Vice President of the Bank and the Company and perform
the duties in connection therewith set forth in Section 4(a).  In addition,
during such third year of the Term the Executive

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shall serve as transitional Chief Executive Officer of the Subsidiary and
perform the duties in connection therewith set forth in Section 4(a) until a
successor Chief Executive Officer of the Subsidiary is appointed during such
third year.

          (c)  During the fourth and fifth years of the Term, the Executive
shall serve as an executive employee of the Bank and shall perform such duties
in connection therewith as may be assigned to him from time to time by the Chief
Executive Officer of the Bank.

          (d)  During the first two years of the Term (except for periods of
illness and vacation), substantially all of the Executive's business time,
attention, skill and efforts shall be devoted to the performance of the
Executive's duties under this Agreement.  During the third year of the Term
(except for periods of illness and vacation), not less than the equivalent of
120 full-time days of the Executive's business time, attention, skill and
efforts shall be devoted to the performance of the Executive's duties under this
Agreement.  During the fourth and fifth years of the Term (except for periods of
illness and vacation), not less than the equivalent of 60 full-time days of the
Executive's business time, attention, skill and efforts shall be devoted to the
performance of the Executive's duties under this Agreement.  During the third,
fourth and fifth years of the Term the Bank shall have the right, in its
discretion, to designate the days or portions thereof on which the Executive
shall be required to perform his duties under this Agreement.  To the extent
that the Executive engages in business activities during the third, fourth and
fifth years of the Term in addition to his duties to the Bank set forth herein,
it is understood and agreed that the Executive shall not engage in any
activities which would materially interfere with his ability to perform his
duties hereunder as requested from time to time by the Bank and shall not
engage, directly or indirectly, as an officer, director, principal, employee,
stockholder or consultant of any

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corporation or other business entity which competes in any material respect with
the businesses carried on by the Bank and its subsidiaries; provided, however,
that the Executive will be permitted to own as a passive investor less than 5%
of any class of publicly-traded securities of any entity which competes with the
Bank and its subsidiaries without being deemed to have violated this Section
4(d). Subject to the foregoing restrictions and to the prior fulfillment of his
obligations to the Bank hereunder, the Executive shall be entitled to perform
consulting services for third parties during the third, fourth and fifth years
of the Term with the prior written approval of the Bank, such approval not to be
unreasonably withheld or delayed.

          5.  Compensation. (a)  The annual salary of the Executive during the
              ------------
first two years of the Term shall be $350,000 which shall, subject to the
provisions of Section 5(g), be payable in installments in accordance with the
prevailing general payroll practice of the Bank as it may exist from time to
time.

          (b)  The annual salary of the Executive during the third year of the
Term shall be at the rate of $250,000 for the equivalent of 120 full-time days
plus $2,500 per day for each full-time equivalent day during such year in excess
of 120 days during which the Executive performs his duties hereunder, which
shall, subject to the provisions of Section 5(g), be payable in installments in
accordance with the prevailing general payroll practice of the Bank as it may
exist from time to time.

          (c) The annual salary of the Executive during the fourth and fifth
years of the Term shall be at the rate of $175,000 for the equivalent of 60
full-time days plus $2,500 per day for each full-time equivalent day during such
years in excess of 60 days during which the Executive performs his duties
hereunder, which shall, subject to the provisions of Section 5(g),

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be payable in installments in accordance with the prevailing general payroll
practice of the Bank as it may exist from time to time.

          (d)  As used in this Agreement, "annual salary" shall mean, at any
time, the annual rate of salary then payable to the Executive pursuant to this
Section 5 (before deduction of any amounts deferred under any deferred
compensation plan of the Bank, any voluntary contributions to the Retirement
401(k) Investment Plan of the Company or other similar qualified plan under
Section 401(a) of the Internal Revenue Code of 1986, as amended (the "Code")
(collectively, the "401(k) Plan"), or any other deductions from income) and
shall be exclusive of bonuses, incentive compensation or other compensation or
benefits paid to or accrued for the Executive other than pursuant to this
Section 5.

          (e)  Solely to the extent that the Executive does not accrue benefits
pursuant to the qualified retirement plans of the Bank or the Benefit
Restoration Plan of The Dime Savings Bank of New York, FSB (the "Benefit
Restoration Plan") with respect to any period during his employment by the Bank
following the second anniversary of this Agreement, and to the extent not
otherwise provided pursuant to Section 11(g)(ii) or 11(g)(iii) or otherwise
limited pursuant to Section 8(c), unless the Executive terminates his employment
prior thereto other than as contemplated by Sections 11(c)(ii) or 11(c)(iii) in
connection with a Change in Control (as defined in Section 11(a)), the Executive
shall be paid, within 120 days of the earlier to occur of (A) the Effective Date
of Termination of the Executive's employment by the Bank (unless such
termination is for "cause," as defined in Section 8(b)), or (B) the fifth
anniversary of the date hereof, a lump sum amount equal to the sum of the
following: (i) the excess of the Present Value (as defined below) of the
benefits the Executive would have accrued and would have a vested

                                       5
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interest in under the Retirement Plan of Dime Bancorp, Inc. (the "Retirement
Plan") and the related provisions of the Benefit Restoration Plan if the
Executive had been otherwise employed as a full-time salaried employee through
the remaining Term at the time of such termination (commencing with the date of
this Agreement) earning the same amount of base pay as the annual salary (as
described in this Section 5) which would have been paid to the Executive over
such remaining Term in accordance with the provisions of this Agreement, over
the Present Value of the benefits the Executive actually accrued under the
Retirement Plan and the related provisions of the Benefit Restoration Plan in
which the Executive has a vested interest, plus (ii) the excess, if any, of the
amount of Bank matching contributions that would have been made and in which the
Executive would have a vested interest under the 401(k) Plan and the related
provisions of the Benefit Restoration Plan, in each instance if the Executive
had been otherwise employed as a full-time salaried employee of the Bank through
the remaining Term at the time of such termination (commencing with the date of
this Agreement) earning the same amount of base pay as the annual salary (as
described in this Section 5) which would have been paid to the Executive over
such remaining Term in accordance with the provisions of this Agreement, and
assuming solely for these purposes that the Executive had made the maximum
contributions permitted under the terms of the 401(k) Plan, over the amount
actually accrued by the Executive with respect to Bank matching contributions
under such 401(k) Plan and the related provisions of the Benefit Restoration
Plan in which the Executive has a vested interest. For these purposes, the
"Present Value" of benefits shall be determined as of the date of the
termination of the Executive's employment with the Bank and shall be calculated
in the same manner as then applies for purposes of determining lump sum benefits
under the Retirement Plan. Further, in

                                       6
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determining the value of benefits described in clause (ii) above, such benefits
shall be credited with the same deemed rate of earnings (or losses) as apply to
the Executive's deemed investments of his 401(k) Plan Restoration Account under
the Benefit Restoration Plan.

          (f)  The Executive shall not have or acquire by virtue of this
Agreement any rights to participate in, or receive benefits with respect to, any
compensation or benefit plan or program of the Bank, except (i) that while
employed by the Bank the Executive may participate in such plans or programs to
the extent provided in such plans and programs and on the same basis as if the
Executive's employment were not subject to the terms and conditions of this
Agreement, or (ii) as otherwise specifically provided in this Agreement.

          (g) Notwithstanding anything to the contrary in the foregoing
provisions, the payment of any amounts that would otherwise be payable to the
Executive but which would be in excess of the amount which the Company, the Bank
or the Subsidiary could deduct for federal income tax purposes if then paid, on
account of the operation of Section 162(m) of the Code, shall be deferred to the
extent that such deferral is required pursuant to a policy adopted by the
Compensation Committee of the Company or the Bank and, to the extent so
deferred, shall be payable pursuant to the relevant terms of the Dime Bancorp,
Inc. Voluntary Deferred Compensation Plan.

          6.  Disability.  (a)  The Bank may terminate the Executive's
              ----------
employment under this Agreement for "permanent disability" if (i) the Executive
shall become physically or mentally disabled or incapacitated to the extent that
the Executive has been absent from the Executive's duties with the Bank on
account of such disabilities or incapacitation as determined in a manner
consistent with the policy which applies generally to employees of the Bank on a

                                       7
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full-time basis for a period of six consecutive months, and (ii) within 30 days
after written notice of proposed termination for permanent disability is given
by the Bank to the Executive, the Executive shall not have returned to full-time
performance of the Executive's duties.

          (b)  In the event of termination for "permanent disability," the Bank
shall continue to pay the Executive an amount equal to the Executive's then
annual salary pursuant to Section 5 (less any benefits that would have been
payable to the Executive had the Executive elected the maximum available amount
of disability insurance coverage available from the Bank) for a period
commencing on the Effective Date of Termination and ending on the first
anniversary thereof (or the end of the remaining Term, if earlier).
Notwithstanding the first sentence of this Section 6(b), any such payment shall
terminate upon the earliest to occur of (A) the date the Executive returns to
the level of employment with the Bank otherwise contemplated by this Agreement;
(B) the Executive's full-time employment by another employer; or (C) the
Executive's death.  In the event of termination for "permanent disability," the
Bank also shall continue to provide until the end of the remaining Term (or the
Executive's earlier death) the same level of life, medical and dental insurance
coverage as is maintained by the Bank for full-time employees of the Bank,
provided that the Executive shall continue to pay all amounts in respect of such
coverage that other employees receiving the same level of coverage are required
to pay.  In the event of a termination of the Executive's employment for
"permanent disability" during the Term at any time following a Change in Control
(as defined in Section 11(a)), the provisions of Section 11 shall apply in lieu
of the provisions of this Section 6(b).

          (c)  There shall be no reduction in the compensation payable to the
Executive or the Executive's other rights under this Agreement during any period
when the Executive is

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incapable of performing some or all of the Executive's duties by reason of
temporary or partial disability.

          7.  Death.  In the event of the Executive's death during the Term,
              -----
this Agreement and all of the Bank's obligations under this Agreement shall
terminate.

          8.  Termination by the Bank.  (a)  The Bank may terminate the
              -----------------------
Executive's employment under this Agreement at any time by giving the Executive
written notice of such termination, provided that, except where termination is
for "cause" (as defined in Section 8(b)), such notice shall be provided at least
30 days prior to the Effective Date of Termination.  In the event of a
termination of the Executive's employment by the Bank, other than a termination
for "cause" (as defined in Section 8(b)), the Bank shall (subject to the
provisions of Section 8(c)) (i) pay to the Executive, as a severance payment for
services previously rendered to the Company and the Bank, a lump sum equal to
the aggregate annual salary (as defined in Section 5(d)) payable to the
Executive with respect to the remainder of the Term as of the Effective Date of
Termination (assuming for this purpose that the Executive performed services
hereunder for no more than the minimum number of full-time equivalent days
required in years three, four and five of the Term) and (ii) maintain the same
level of life, medical and dental insurance coverage as is maintained by the
Bank for full-time employees of the Bank, provided that the Executive shall
continue to pay all amounts in respect of such coverage that other employees
receiving the same level of coverage are required to pay, for the remainder of
the Term as of the Effective Date of Termination (or the Executive's earlier
death).  Notwithstanding the foregoing, such life, medical and dental insurance
coverage shall cease upon the Executive's employment by another employer which
provides coverage for the Executive which is no less favorable (in benefits and

                                       9
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duration) than that provided by the Bank (and if provided for a lesser duration,
shall cease during the period such coverage is provided by another employer).
In the event of a termination of the Executive's employment by the Bank during
the Term following a Change in Control, the provisions of Section 11 shall apply
in lieu of the provisions of this Section 8(a).

          (b)  The Executive shall have no right to receive compensation or
other benefits under this Agreement for any period after the Effective Date of
Termination if the Executive's employment is terminated for cause.  As used in
this Agreement, "cause" shall mean the Executive's personal dishonesty,
incompetence, willful misconduct, breach of fiduciary duty involving personal
profit, intentional failure to perform assigned duties, willful violation of any
law, rule or regulation (other than traffic violations or similar offenses) or
final cease and desist order or material breach of any provision of this
Agreement.

          (c) (i)  Notwithstanding any other provision of this Section 8 or of
Section 11, if at the Effective Date of Termination any statute, regulation,
order, agreement, or regulatory interpretation thereof that is valid and binding
upon the Bank (a "Regulatory Restriction") shall restrict, prohibit or limit the
amount of any payment or the provision of any benefit that the Bank would
otherwise be liable for under this Section 8 or under Section 11, then the
amount that the Bank shall pay to the Executive hereunder shall not exceed the
maximum amount permissible under such Regulatory Restriction; provided, that if
such Regulatory Restriction shall subsequently be rescinded, superseded, amended
or otherwise determined not to restrict, limit or prohibit payment by the Bank
of amounts otherwise due the Executive hereunder, then the Bank shall promptly
thereafter pay to such Executive any amounts (or the value of any benefit)
previously withheld from such Executive as a result of such Regulatory
Restriction.

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          (ii) Notwithstanding any other provision of this Section 8 or of
Section 11, in the event that any amount otherwise payable hereunder other than
on account of events following a Hostile Change in Control (as hereinafter
defined) would be deemed to constitute a parachute payment (a "Parachute
Payment") within the meaning of Section 280G of the Code, and if any such
Parachute Payment, when added to any other payments which are deemed to
constitute Parachute Payments, would otherwise result in the imposition of an
excise tax under Section 4999 of the Code, the amounts payable hereunder (other
than amounts payable on account of events following a Hostile Change in Control)
shall be reduced by the smallest amount necessary to avoid the imposition of
such excise tax.  Any such limitation shall be applied to such compensation and
benefit amounts, and in such order, as the Bank shall determine in its sole
discretion.  References to the Code in this Agreement shall be to the Code as
presently in effect or to the corresponding provisions of any succeeding law

          (d) As of the date hereof, the principal place of business at which
the Executive shall be based for the performance of his duties pursuant to this
Agreement is located in Tampa, Florida.  If the Bank shall relocate such
principal place of business at which the Executive shall be based to a location
which is more than 75 miles from Tampa, Florida, the Executive shall have the
right, for a period of 30 days following such relocation, to elect to treat such
relocation as a termination of the Executive's employment by the Bank without
cause (as defined in Section 8(b)) by giving the Bank written notice of such
election.  In the event that the Executive fails to give notice within such 30-
day period, he shall be deemed to have waived his right to make such an election
with respect to such relocation.

          (e) Upon the termination of the Executive's employment by the Bank
pursuant to

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the provisions of this Section 8, to the extent not otherwise limited by Section
8(c) and except where termination is for "cause" (as defined in Section 8(b)),
each outstanding Non-Accelerated Stock Option (as defined in Section 11(d)(ii))
and each share of restricted stock which has not previously vested that is held
by the Executive shall (to the extent permitted by the plan under which such
Non-Accelerated Stock Option or restricted stock was granted), notwithstanding
anything to the contrary in the grant letter related to such Non-Accelerated
Stock Option or restricted stock and regardless of the actual Effective Date of
Termination, immediately vest and become exercisable, in the case of a Non-
Accelerated Stock Option, and immediately vest, in the case of restricted stock.

          (f) If the Executive's employment is proposed to be terminated by the
Bank for "cause" (as defined in Section 8(b)), the Bank shall, prior to
delivering to the Executive a notice of termination, afford the Executive
reasonable prior notice of such proposed termination and an opportunity for him,
together with counsel, to be heard.

          9.  Voluntary Termination by the Executive.  The Executive shall have
              --------------------------------------
the right to terminate the Executive's employment under this Agreement at any
time upon at least 30 but not more than 60 days' prior written notice to the
Bank.  If this Agreement is terminated pursuant to the immediately preceding
sentence, all of the Bank's obligations under this Agreement shall terminate and
the Executive shall not be entitled to any compensation or benefits after the
Effective Date of Termination, except to the extent provided in Section 11.

          10.  Additional Termination and Suspension Provisions.  (a) If the
               ------------------------------------------------
Executive is removed and/or permanently prohibited from participating in the
conduct of the Bank's affairs by an order issued under Section 8(e)(4) or (g)(1)
of the Federal Deposit Insurance Act (12 U.S.C.

                                       12
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1818(e)(4) or (g)(1)), all obligations of the Bank under this Agreement shall
terminate as of the effective date of the order, but vested rights of the
parties shall not be affected.

          (b)  If the Bank is in default (as defined in Section 3(x)(1) of the
Federal Deposit Insurance Act), all obligations under this Agreement shall
terminate as of the date of default, but this paragraph shall not affect any
vested rights of the parties.

          (c)  All obligations under this Agreement shall be terminated, except
to the extent determined that continuation of this Agreement is necessary for
the continued operation of the Bank, (i) by the Director of Thrift Supervision
or his or her designee (the "Director"), at the time the Federal Deposit
Insurance Corporation enters into an agreement to provide assistance to or on
behalf of the Bank under the authority contained in Section 13(c) of the Federal
Deposit Insurance Act; or (ii) by the Director, at the time the Director
approves a supervisory merger to resolve problems related to operation of the
Bank or when the Bank is determined by the Director to be in an unsafe or
unsound condition.  Any rights of the parties that have already vested, however,
shall not be affected by such action.

          (d)  If the Executive is suspended and/or temporarily prohibited from
participating in the conduct of the Bank's affairs by a notice served under
Section 8(e)(3) or (g)(1) of the Federal Deposit Insurance Act (12 U.S.C.
1818(e)(3) and (g)(1)), the Bank's obligations under this Agreement shall be
suspended as of the date of service unless stayed by appropriate proceedings.
If the charges in the notice are dismissed, the Bank may in its discretion (a)
pay the Executive all or part of the compensation withheld while its contract
obligations were suspended and (b) reinstate (in whole or in part) any of its
obligations which were suspended.

          (e)  The provisions of paragraphs (a) through (d) of this Section 10
are required to

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be set forth in this Agreement by regulations applicable to the Bank on the date
of this Agreement. If any such regulation shall hereafter be amended or
modified, or if any new regulation applicable to the Bank and effective after
the date of this Agreement shall require the inclusion in this Agreement of a
provision not presently included in this Agreement, then the foregoing
provisions of paragraphs (a) through (d) of this Section 10 shall be deemed
amended to the extent necessary to give effect in this Agreement to any such
amended, modified or new regulation.

          11.  Change in Control.  (a) As used in this Agreement, a "Change in
               -----------------
Control" of the Bank shall mean (i) the merger, consolidation or reorganization
of the Bank or the Company with any other entity (or the issuance by the Bank or
the Company of its voting securities as consideration in a merger, consolidation
or reorganization of a subsidiary of the Bank or the Company with any other
entity) whether or not such merger, consolidation or reorganization shall have
been affirmatively recommended to the Bank's stockholders or the Company's
stockholders by action of the Board of Directors of the Bank or the Company,
respectively, other than such a merger, consolidation or reorganization which
would result in the voting securities of the Bank or the Company (as the case
may be) outstanding immediately prior thereto continuing to represent (either by
remaining outstanding or by being converted into voting securities of the other
entity) at least 65% of the combined voting power of the voting securities of
the Bank or the Company (as the case may be) or such other entity outstanding
immediately after such merger, consolidation or reorganization; (ii) the
approval by the stockholders of the Bank or the stockholders of the Company of a
plan of complete liquidation of the Bank or the Company, respectively (a "Plan
of Liquidation"), or an agreement for the sale or

                                       14
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disposition by the Bank or the Company of all or substantially all of the Bank's
assets or the Company's assets (an "Asset Sale Agreement"); (iii) the
acquisition of more than 35% of the voting power of the Bank or the Company by
any person or entity or any persons or entities acting as a group for purposes
of Section 13(d) of the Securities Exchange Act of 1934, as amended; (iv) the
occurrence of any circumstance having the effect that directors who were
nominated for election as directors by the Governance and Nominating Committee
of the Board of Directors of the Bank or the Company shall cease to constitute a
majority of the authorized number of directors of the Bank or the Company,
respectively; or (v) the execution by the Bank or the Company of a binding
agreement that, if consummated, would result in a Change in Control of the type
specified in clause (i) or (iii) of this Section 11(a) (an "Acquisition
Agreement") or of an Asset Sale Agreement or the adoption by the Board of
Directors of the Bank or the Company of a Plan of Liquidation; provided however,
that a Change in Control of the type specified in this clause (v) shall not be
deemed to exist or have occurred as a result of the execution of such
Acquisition Agreement or Asset Sale Agreement, or the adoption of such a Plan of
Liquidation, from and after the Abandonment Date if the Executive's employment
has not been terminated on or prior to the Abandonment Date. As used in this
Section 11(a), the term "Abandonment Date" shall mean the date on which (A) an
Acquisition Agreement, Asset Sale Agreement or Plan of Liquidation is terminated
(pursuant to its terms or otherwise) without having been consummated, (B) the
parties to an Acquisition Agreement or Asset Sale Agreement abandon the
transactions contemplated thereby, (C) the Bank or the Company abandons a Plan
of Liquidation or (D) a court or regulatory body having competent jurisdiction
enjoins or issues a cease and desist or stop order with respect to or otherwise
prevents the consummation of, or a

                                       15
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regulatory body notifies the Bank or the Company that it will not approve, an
Acquisition Agreement, Asset Sale Agreement or Plan of Liquidation or the
transactions contemplated thereby and such injunction, order or notice has
become final and not subject to appeal. As used in this Agreement, a "Hostile
Change in Control" shall mean (i) any of the events specified in Section
11(a)(i) if such transaction has not been affirmatively recommended to the
Company's stockholders by action of the Board of Directors of the Company or
(ii) any of the events specified in Section 11(a)(i) through (a)(iv) inclusive
if the Board of Directors of the Company or the Bank, as the case may be, finds
that, for purposes of this Agreement, the happening of an event specified in
such Sections constitutes or will constitute a Hostile Change in Control;
provided, however, that if it is an express condition precedent to the
consummation of any such Change in Control event or occurrence that the Board of
Directors of the Company or the Bank, as the case may be, refrain from making
such a designation, the event or occurrence shall constitute a "Hostile Change
in Control" without regard to any designation by the Board of Directors of the
Company or the Bank, as the case may be.

          (b)  If the Bank, the Company or the Subsidiary shall relocate the
principal place of business at which the Executive shall be based for the
performance of his duties pursuant to this Agreement to a location which is more
than 75 miles from Tampa, Florida after a Change in Control of the Bank or the
Company, respectively, and if the Executive shall, as a result, be required to
change the Executive's principal residence, the Bank shall (i) promptly pay (or
reimburse the Executive for) all reasonable moving expenses incurred by the
Executive as a result of such change in the Executive's principal residence, and
(ii) indemnify the Executive against, and reimburse the Executive for, any loss
incurred as a result of the sale of the

                                       16
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Executive's principal residence (which loss shall be computed for the purpose of
this Agreement as the difference between the actual sales price (net of closing
costs and brokerage fees) of such residence and the fair market value of such
residence (computed as of the time such principal place of business is
relocated) as determined by an independent real estate appraiser designated and
paid by the Bank or the Company and acceptable to the Executive), provided that
such sale of the Executive's principal residence occurs within six months after
the Bank, the Company or the Subsidiary relocates the principal place of
business at which the Executive shall be based.

          (c)  (i) If a Change in Control shall occur, the Executive shall be
entitled to the compensation and benefits provided in paragraphs (d), (e), (f)
and (g) of this Section 11 upon the subsequent termination of the Executive's
employment, at any time during the remaining Term in effect at the time of the
Change in Control, by the Bank (including, without limitation, a termination for
permanent disability), other than a termination for cause, provided that the
rights to any such compensation and benefits shall be subject to the limitations
and provisions set forth in Section 8(c).

          (ii)  If a Change in Control (other than a Change in Control of the
type specified in (A) Section 11(a)(i) and (I) that has been affirmatively
                                       ---
recommended to the Company's stockholders by action of the Board of Directors of
the Company, and (II) immediately after giving effect to which, the voting
             ---
securities of the Company outstanding immediately prior thereto continue to
represent (either by remaining outstanding or by being converted into voting
securities of the entity into which the Company has been merged, consolidated or
reorganized) at least 50% of the combined voting power of the voting securities
of the Company or such other entity outstanding immediately after such merger,
consolidation or reorganization, and (III) that
                                 ---

                                       17
<PAGE>

does not constitute a Change in Control under any of subparagraphs 11(a)(ii),
(iii) or (iv); or (B) Section 11(a)(v)) shall occur, the Executive shall be
entitled to the compensation and benefits provided in paragraphs (d), (e), (f)
and (g) of this Section 11 (subject to the limitations and provisions set forth
in Section 8(c)) upon the subsequent termination of the Executive's employment,
at any time within the earlier to occur of 90 days after the occurrence of such
Change in Control and the expiration of the remaining Term in effect at the time
of the Change in Control, by the Executive.

          (iii)  If (A) a Change in Control shall occur, and thereafter the Bank
(notwithstanding its right to do so under Section 4 or Section 5) either (B)
makes a material change in the Executive's functions, duties or
responsibilities, which change would cause the Executive's position with the
Bank to become one of lesser responsibility, importance or scope from that
otherwise contemplated by this Agreement, or (C) reduces the Executive's annual
salary below that otherwise contemplated by this Agreement (an event specified
in clause (B) or (C) is hereafter referred to as a "Material Change"), the
Executive shall be entitled to the compensation and benefits provided in
paragraphs (d), (e), (f) and (g) of this Section 11 (subject to the limitations
and provisions set forth in Section 8(c)) upon the subsequent termination of the
Executive's employment, at any time during the remaining Term in effect at the
time of the Change in Control, by the Executive.

          (iv)  Only for purposes of determining whether there has been a
termination of the Executive's employment during the remaining Term in effect at
the time of a Change in Control or within 90 days after the occurrence of a
Change in Control (as specified in paragraphs (c)(i), (c)(ii) and (c)(iii) of
this Section 11, as the case may be) so as to entitle the Executive to the

                                       18
<PAGE>

compensation and benefits provided in paragraphs (d), (e), (f) and (g) of this
Section 11, a termination of the Executive's employment following a Change in
Control shall be deemed to have occurred on such date during the remaining Term
that notice of termination is given by the Bank or the Executive to the other
(regardless of the Effective Date of Termination specified in such notice).
Notwithstanding the immediately preceding sentence, the Executive shall continue
to be employed by the Bank pursuant to this Agreement until the Effective Date
of Termination specified in the notice of termination.

          (d)(i)  Upon the occurrence of a Change in Control followed by any
termination of the Executive's employment pursuant to Section 11(c)(i), (c)(ii)
or (c)(iii), to the extent not otherwise limited pursuant to Section 8(c), the
Bank shall pay the Executive, as a severance payment for services previously
rendered to the Bank, a lump sum equal to three times the Executive's annual
salary (as defined in Section 5(d)) (assuming for this purpose that the
Executive performed services hereunder for no more than the minimum number of
full-time equivalent days required in each of years three, four and five of the
Term).

          (ii)  Upon the occurrence of (a) the termination of the Executive's
employment by the Bank (unless such termination is for "cause" as defined in
Section 8(b)) or (b) a Change in Control which is not a Hostile Change in
Control followed by any termination of the Executive's employment pursuant to
Section 11(c)(i), (c)(ii) or (c)(iii), to the extent not otherwise limited
pursuant to Section 8(c): (A) each Non-Accelerated Stock Option held by the
Executive shall (to the extent permitted by the plan under which such Non-
Accelerated Stock Option was granted), notwithstanding anything to the contrary
in the grant letter related to such Non-Accelerated Stock Option and regardless
of the actual Effective Date of Termination, vest and become exercisable

                                       19
<PAGE>

in accordance with the provisions of, and remain exercisable for the term
specified in, such grant letter as if there had been no termination of the
Executive's employment and the Executive remained in the employment of the Bank
for the entire term of such Non-Accelerated Stock Option and (B) each Vested
Stock Option held by the Executive shall (to the extent permitted by the plan
under which such Vested Stock Option was granted), notwithstanding anything to
the contrary in the grant letter related to such Vested Stock Option and
regardless of the actual Effective Date of Termination, remain exercisable for
the term specified in such grant letter as if there had been no termination of
the Executive's employment and the Executive remained in the employment of the
Bank for the entire term of such Vested Stock Option. As used in this Section
11(d)(ii) and Section 11(d)(iii), the term (I) "Non-Accelerated Stock Option"
shall mean any stock option (including any tandem stock appreciation right)
previously or hereafter granted to the Executive under a stock incentive or
stock option plan of the Company that has not, pursuant to the provisions of
such stock incentive or stock option plan or the grant letter pursuant to which
such stock option was granted to the Executive, vested and become exercisable
prior to the Effective Date of Termination and (II) "Vested Stock Option" shall
mean any stock option (including any tandem stock appreciation right) previously
or hereafter granted to the Executive under a stock incentive or stock option
plan of the Company that vests and becomes exercisable prior to the Effective
Date of Termination.

          (iii) Upon the occurrence of a Hostile Change in Control followed by
any termination of the Executive's employment pursuant to Section 11(c)(i),
(c)(ii) or (c)(iii), to the extent not otherwise limited pursuant to Section
8(c)(i): (A) each Non-Accelerated Stock Option held by the Executive shall (to
the extent permitted by the plan under which such Non-

                                       20
<PAGE>

Accelerated Stock Option was granted), notwithstanding anything to the contrary
in the grant letter related to such Non-Accelerated Stock Option and regardless
of the actual Effective Date of Termination, immediately vest and become
exercisable in accordance with the provisions of, and remain exercisable for the
term specified in, such grant letter as if there had been no termination of the
Executive's employment and the Executive remained in the employment of the Bank
for the entire term of such Non-Accelerated Stock Option and (B) each Vested
Stock Option held by the Executive shall (to the extent permitted by the plan
under which such Vested Stock Option was granted), notwithstanding anything to
the contrary in the grant letter relating to such Vested Stock Option and
regardless of the actual Effective Date of Termination, remain exercisable for
the term specified in such grant letter as if there had been no termination of
the Executive's employment and the Executive had remained in the employment of
the Bank for the entire term of such Vested Stock Option.

          (iv) Upon the occurrence of (a) the termination of the Executive's
employment by the Bank (unless such termination is for "cause" as defined in
Section 8(b)) or (b) a Change in Control followed by any termination of the
Executive's employment pursuant to Section 11(c)(i), (c)(ii) or (c)(iii), to the
extent not otherwise limited pursuant to Section 8(c), each grant of restricted
stock to the Executive shall (to the extent permitted by the plan under which
such restricted stock was granted), notwithstanding anything to the contrary in
the grant letter related to such restricted stock, vest and become non-
forfeitable by the Executive as if there had been no termination of the
Executive's employment and the Executive remained in the employment of the Bank
for the entire term of the vesting period applicable to such grant of restricted
stock.

          (e)  Any payment pursuant to Section 11(d)(i) or 11(g)(iii) shall be
made to the

                                       21
<PAGE>

Executive within 30 days after the Effective Date of Termination.

          (f)  Upon the occurrence of a Change in Control followed by any
termination of the Executive's employment pursuant to Section 11(c)(i), (c)(ii)
or (c)(iii), to the extent not otherwise limited pursuant to Section 8(c), the
Bank shall cause to be continued until the end of the remaining Term (or the
Executive's earlier death) the same level of life, disability, medical and
dental insurance coverage as is maintained by the Bank for full-time employees
of the Bank, provided that the Executive shall continue to pay all amounts in
respect of such coverage that other employees receiving the same levels of
coverage are required to pay.

          (g)(i) In the event of termination of the Executive's employment
pursuant to Section 11(c)(i), (c)(ii) or (c)(iii), to the extent not otherwise
limited pursuant to Section 8(c), the Executive shall vest in the benefits under
Section 5(e) hereof (but which shall then be calculated assuming that the
benefits payable under the Retirement Plan, the 401(k) Plan and the Benefit
Restoration Plan are fully vested).

          (ii)  In the event of termination of the Executive's employment
pursuant to Section 11(c)(i), (c)(ii) or (c)(iii), to the extent not otherwise
limited pursuant to Section 8(c), the Executive shall be entitled to receive a
benefit calculated pursuant to the provisions of the Retirement Plan as in
effect immediately prior to the Change in Control (or, if more favorable to the
Executive, as in effect immediately prior to the Effective Date of Termination),
(A) without regard to any limitations set forth in such plan pursuant to
Sections 401(a)(17) and 415 of the Code, and (B) assuming that the Executive's
service at the Effective Date of Termination was sufficient to vest the
Executive 100% in the benefit accrued under such plan.  The benefit provided for
in the preceding sentence (stated in the form of a single life annuity or such
other

                                       22
<PAGE>

normal form of benefit as may be provided on an unreduced basis under the
Retirement Plan) shall be offset by the benefit payable to the Executive and the
Executive's beneficiaries (stated in the form of a single life annuity or such
other normal form of benefit as may be provided on an unreduced basis) under the
Retirement Plan (without regard to benefit reductions in that plan on account of
benefits payable under qualified defined contribution plans, if any) and the
Benefit Restoration Plan (solely to the extent the Benefit Restoration Plan
supplements benefits under the Retirement Plan).  The benefit provided pursuant
to this Section 11(g)(ii) shall be payable at the same time and in the same form
as benefits are payable to the Executive and the Executive's beneficiaries under
the Benefit Restoration Plan that relate to Retirement Plan benefits (or would
be so payable if the Executive were vested under such Plan).  Except for the
offset contemplated in this Section 11(g)(ii), the benefit provided for in this
Section 11(g)(ii) shall be in addition to any benefits payable under any
qualified or non-qualified pension plans or programs maintained by the Bank.  If
the Executive's termination of employment following a Material Change occurs by
reason of the Executive's death, to the extent not otherwise limited pursuant to
Section 8(c), the Executive's surviving spouse shall receive an annuity payable
for the remainder of such spouse's lifetime equal to 100% of the benefit such
spouse would have received had the Executive retired the day before the
Executive's death and elected to have the Executive's pension benefit payable
pursuant to this Section 11(g)(ii) paid, commencing upon such retirement, in the
form of a 100% contingent annuity.  Upon such surviving spouse's death, such
benefit shall be paid to the Executive's children in the manner described in
Section 5.4 of the Retirement Plan.

          (iii)  In the event of termination of the Executive's employment
pursuant to

                                       23
<PAGE>

Section 11(c)(i), (c)(ii) or (c)(iii), to the extent not otherwise
limited pursuant to Section 8(c), the Executive shall be entitled to receive in
a lump sum payment an amount equal to any amounts forfeited by the Executive
under the 401(k) Plan and under the Benefit Restoration Plan (solely to the
extent such Benefit Restoration Plan supplements benefits under the 401(k) Plan)
as in effect immediately prior to the Change in Control (or, if more favorable
to the Executive, as in effect immediately prior to the Effective Date of
Termination).

          (h)(i) If, following a Hostile Change in Control, any payment or other
benefit paid or to be paid or any property transferred or to be transferred
(collectively, a "Severance Payment") with respect to one or more calendar years
by or on behalf of the Bank (or any affiliate of the Bank) to the Executive
pursuant to this Agreement shall constitute an "excess parachute payment" within
the meaning of Section 280G(b) of the Code subject to the tax imposed by Section
4999 of the Code (the "Excise Tax"), then the Bank shall pay to the Executive an
additional amount (the "Gross Up Payment") such that the amount paid or
transferred to the Executive, after deduction of any Excise Tax on the Severance
Payment, and any federal, state and local income tax, employment tax and Excise
Tax upon the Gross Up Payment, shall be equal to the Severance Payment.

          (ii)   For purposes of determining under Section 11(h)(i) whether any
portion of a Severance Payment will be subject to the Excise Tax and the amount
of such Excise Tax, (A) the Severance Payment and payment provided for in
Section 11(h)(i) shall be treated as "parachute payments" within the meaning of
Section 280G(b)(2) of the Code, and all "excess parachute payments" within the
meaning of Section 280(G)(b)(1) of the Code shall be treated as subject to the
Excise Tax, unless and to the extent that tax counsel selected by the Bank's
independent

                                       24
<PAGE>

auditors and acceptable to the Executive is of the opinion that the Severance
Payment (in whole or in part) does not constitute a "parachute payment" or such
"excess parachute payment" (in whole or in part) represents reasonable
compensation for services actually rendered within the meaning of Section
280G(b)(4) of the Code in excess of the allocable base amount within the meaning
of Section 280G(b)(3) of the Code, or the Severance Payment is otherwise not
subject to the Excise Tax, (B) the amount of the Severance Payment that is
treated as subject to the Excise Tax shall be equal to the lesser of (X) the
total amount of the Severance Payment and (Y) the amount of "excess parachute
payments" within the meaning of Section 280G(b)(1) of the Code (after applying
clause (A) above), (C) any Gross Up Payment pursuant to Section 11(h)(i) shall
be treated as subject to the Excise Tax in its entirety and (D) the value of any
non-cash benefits or any deferred payment or benefit shall be determined by the
Company's independent auditors in accordance with the principles of Sections
280G(d)(3) and (4) of the Code.

          (iii) If in circumstances described in Section 11(h)(i), by reason of
the filing by the Executive of an amended tax return, an audit by the Internal
Revenue Service or other taxing authority, or a final determination by a court
of competent jurisdiction, it is determined that "excess parachute payments"
exceeding those previously reported in his tax returns were received by the
Executive and as a result an additional Excise Tax (the "Additional Excise Tax")
shall become due, the Bank shall pay the Executive an additional amount (the
"Subsequent Gross Up Payment") such that the amount paid or transferred to the
Executive after deduction of (A) any Additional Excise Tax and (B) on an after
tax basis, any interest, additions and penalties with respect to the Additional
Excise Tax and (C) any federal, state and local income tax, employment tax and
Excise Tax upon the Subsequent Gross up Payment and (D) the payments provided
for in

                                       25
<PAGE>

Section 11(h)(i), shall be equal to the Severance Payment.

          (iv) Any Gross Up Payment required hereunder shall be made at least
ten days prior to the due date (without regard to extensions) of the Executive's
federal income tax return for the year with respect to which the "excess
parachute payment" is deemed made under the Code.  Any Subsequent Gross Up
Payment required hereunder shall be made to the Executive within 30 days after
the amount thereof is determined.  Notwithstanding the two immediately preceding
sentences, the Bank shall pay any federal, state and local tax or taxes and
employment taxes required to be withheld from the Executive's wages (within the
meaning of Section 3121 and 3402 of the Code) with respect to the "excess
parachute payment" and any such tax or taxes paid by the Company, the Bank or
the Subsidiary to the Internal Revenue Service or state or local taxing
authority shall constitute payment to the Executive

          (v) If the Excise Tax is finally determined (whether by the filing of
an amended tax return by the Executive, by audit of the Internal Revenue Service
or other taxing authority, or by a final determination of a court of competent
jurisdiction) to be less than the amount paid to or on behalf of the Executive
under the provisions of Sections 11(h)(i)-(iv) and the overpayment is refunded
to the Executive, the Executive shall repay to the Bank, promptly following the
receipt of the refund, the portion of the Gross Up Payment (and/or Subsequent
Gross Up Payment) attributable to such reduction of the Excise Tax (plus the
portion attributable to federal, state and local income tax and employment taxes
imposed on the portion being repaid by the Executive but only to the extent that
the repayment may result in a tax benefit to the Executive under Section 1341 of
the Code and similar provisions of applicable state and local law).

          (vi) The provisions of this Section 11(h) shall inure to the benefit
of the Executive

                                       26
<PAGE>

during the Term of this Agreement regardless of whether or not his employment is
terminated, and if the Executive's employment is terminated, the rights and
obligations of the Executive and the Bank under this Section 11(h) shall survive
the termination of this Agreement.

          12.  Post-Termination Obligations of the Executive.  (a) Upon any
               ---------------------------------------------
termination of the Executive's employment during the Term of this Agreement or
upon termination of the Executive's employment after the expiration of the Term
of this Agreement or upon retirement, the Executive agrees (i) not to make any
disclosure in violation of Section 12(b), (ii) to return to the Bank all
material documents relating to the business of the Company, the Bank, the
Subsidiary and their affiliates that are in the Executive's possession or under
the Executive's control, and (iii) except if the termination or retirement
occurs after a Change in Control, not to solicit (directly or indirectly), for
one year following the Effective Date of Termination (or date of termination
after the expiration of the Term) or retirement, the employment of any person
who is an employee of the Company, the Bank, the Subsidiary or their affiliates
on the Effective Date of Termination (or date of termination after the
expiration of the Term) or retirement or who, within six months prior to the
Effective Date of Termination (or date of termination after the expiration of
the Term) or retirement, was an employee of the Company, the Bank, or Subsidiary
or their affiliates, unless the Executive receives written permission from the
Bank to engage in the activities proscribed by this Section 12(a) or by Section
12(b) or to be relieved of any obligation under Section 12(a)(ii).

          (b)  The Executive recognizes and acknowledges that the confidential
business activities and plans for business activities of the Bank and its
subsidiaries and affiliates, as they may exist from time to time, are valuable,
special and unique assets of the Bank.  The Executive

                                       27
<PAGE>

shall not, during or at any time after the Executive's employment, disclose any
knowledge of the past, present or planned business activities of the Bank or its
subsidiaries or affiliates that are of a confidential nature (collectively, the
"Bank's Confidential Activities") to any person, firm, corporation, bank, thrift
institution or other entity for any reason or purposes whatsoever.
Notwithstanding anything in this Section 12(b) to the contrary, the Executive
(i) may disclose any knowledge of banking, financial and/or economic principles,
concepts or ideas that are not derived from the Bank's Confidential Activities,
and (ii) shall not be precluded from disclosures respecting the Bank's
Confidential Activities that are (A) made pursuant to compulsory legal process
or when required by an appropriate governmental agency; (B) public knowledge or
become public without the Executive's breach of this Section 12(b); (C) already
known to the party to whom the Executive makes such disclosures; or (D) approved
by the Bank for disclosure.

          (c)  The parties, recognizing that irreparable injury will result to
the Bank, its business and property in the event of the Executive's breach or
threatened breach of Section 12(a) or (b), agree that in the event of such
breach or threatened breach by the Executive, the Bank will be entitled, in
addition to any other remedies and damages that may be available, to seek and
obtain an injunction to restrain the violation of Section 12(a) or (b) by the
Executive.

          13.  Notices.  All notices under this Agreement shall be in writing
               -------
and shall be delivered personally or sent by registered or certified mail,
return receipt requested, (a) to the Bank, at its address set forth above (to
the attention of its Chief Executive Officer) and (b) to the Executive, at the
Executive's residence address as appearing in the records of the Bank, or to
such other address as either party may hereafter designate in writing in the
manner provided in

                                       28
<PAGE>

this Section 13. All notices under this Agreement shall be deemed given (i) upon
receipt if delivered personally or (ii) two days after deposit in a facility of
the U.S. Postal Service with postage prepaid. As used in this Agreement, the
term "Effective Date of Termination" shall mean the date specified in a notice
hereunder on which such Executive's employment is to terminate, provided,
however, that no such notice shall specify an Effective Date of Termination that
is prior to the date on which any such notice is given.

          14.  Complete Understanding.  This Agreement, together with the
               ----------------------
Agreement Regarding Initial Employment Terms attached hereto as Exhibit A,
constitute the complete understanding between the parties with respect to the
subject matter hereof and thereof and merge and supersede all prior oral and
written agreements and understandings and all contemporaneous oral agreements
and understandings with respect to the subject matter hereof and thereof,
including, without limitation, any other employment agreement heretofore
executed by the Executive and the Bank or any of its subsidiaries or affiliates.
In the event of any conflict between the express provisions of this Agreement
and such Agreement Regarding Initial Employment Terms, the express provisions of
this Agreement shall be controlling.  This Agreement may not be amended,
terminated or rescinded except in a writing signed by the party to be charged.

          15.  No Waiver.  The failure of either party at any time to require
               ---------
performance by the other party of a provision of this Agreement or to resort to
a remedy at law or in equity or otherwise shall in no way affect the right of
such  party to require full performance or to resort to such remedy at any time
thereafter nor shall a waiver by either party of the breach of any provision of
this Agreement be taken or held to be a waiver of any subsequent breach of such

                                       29
<PAGE>

provision unless expressly so stated in writing.  No waiver of any of the
provisions of this Agreement shall be effective unless in writing and signed by
the party to be charged.

          16.  Governing Law.  This Agreement shall be governed by the laws of
               -------------
the State of New York, without regard to conflict of laws principles applied in
the State of New York.

          17.  Headings.  The headings to the Sections of this Agreement are for
               --------
convenience of reference only and shall not be given any effect in the
construction or interpretation of this Agreement.

          18.  Severability.  If any provision of this Agreement is held by a
               ------------
court or other authority having competent jurisdiction to be invalid, void or
otherwise unenforceable, in whole or in part, by reason of any applicable law,
statute or regulation or any interpretation thereof, then (a) the remainder of
the provisions of this Agreement shall remain in full force and effect and in no
way be affected, impaired or invalidated and (b) the provision so held to be
invalid, void or otherwise unenforceable shall be deemed modified in amount,
duration, scope or otherwise to the minimum extent necessary so that such
provision shall not be invalid, void or otherwise unenforceable by reason of
such law, statute, regulation or interpretation and such provision, as so
modified, shall remain in full force and effect.

          19.  Payment of Legal Fees.  If any legal action or proceeding is
               ---------------------
commenced to enforce or interpret the provisions of this Agreement, or to
recover damages for its breach, all reasonable legal fees, disbursements and
court costs paid or incurred by the Executive arising out of or resulting from
such action or proceeding shall be paid or reimbursed to the Executive by the
Bank, provided the Executive shall be the prevailing party in such action or
proceeding.

          20.  Assumption by Company.  This Agreement shall be assumable by the
               ---------------------

                                       30
<PAGE>

Company at its election.  Following any such election, the obligations of the
Bank under this Agreement shall become the obligations of the Company.

          21.  Taxes.  Any payments due to the Executive pursuant to this
               -----
Agreement shall be reduced by all applicable federal, state, city or other taxes
required by law to be withheld with respect to such payments.

          22.  Limitation on Payments.  Any payments made to the Executive
               ----------------------
pursuant to this Agreement, or otherwise, are subject to and conditioned upon
their compliance with 12 USC (S) 1828(k) and any regulations promulgated
thereunder.


                         THE DIME SAVINGS BANK
                         OF NEW YORK, FSB


                         By: /s/ Lawrence J. Toal
                             -------------------------------------
                                Name:
                                Title:



Dated: 2/27/97               /s/ Fred B. Koons
       -------------         ------------------------------------
                                 FRED B. KOONS

                                       31
<PAGE>

             [Letterhead of The Dime Savings Bank of New York, FSB]


                                              As of December 2, 1996

Mr. Fred B. Koons
3308 Jean Circle
Tampa, Florida 33629


          Re:  Agreement Regarding Initial Employment Terms
               --------------------------------------------

Dear Fred:

          As we discussed, this Letter Agreement is intended to detail several
elements of your initial compensation arrangements with The Dime Savings Bank of
New York, FSB (the "Bank").  To the extent, however, that it describes benefits
requiring the approval of the Compensation Committee or the Board of Directors
of the Bank or of Dime Bancorp, Inc. (the "Company"), it is subject to that
approval, and to changes that may be determined by such Committee(s) or such
Board(s) from time to time, and participation in the various plans described
will be pursuant to the terms of those plans, as they may be revised (and
subject to their termination) from time to time by the Bank or the Company.  The
benefits described herein are also subject to other limitations described in
further detail below.  As of the date hereof, all of the benefits set forth
below are permitted by the terms of the various plans described.

          1.   Restricted Stock Award  As soon as possible following the date
               ----------------------
hereof, you will be awarded the right to purchase such number of whole shares of
restricted stock pursuant to the Dime Bancorp, Inc. 1991 Stock Incentive Plan
(the "Plan") as shall have an aggregate value on the date of award of
approximately $350,000, with such restricted stock vesting 50% on the first
anniversary of the date hereof and 50% on the second anniversary of the date
hereof, subject to earlier vesting under the circumstances described in section
15.1 of the Plan.  The purchase price for each share of restricted stock,
described in the preceding sentence, shall be equal to $1.00 per share.  The
Company agrees to pay to you an amount equal to the sum of: (i) the aggregate
purchase price for the restricted stock awarded hereunder and (ii) the Federal,
state and local income tax liability that the Bank determines would arise from
the payment referred to in (i).

          2.   Annual Incentive Opportunity.  You will be eligible to
               ----------------------------
participate in the Bank's Officer Incentive Plan during 1998, with a target
incentive opportunity of $100,000, and the opportunity to earn up to 150% of
such target incentive based on extraordinary performance. The final
determination of the incentive to be paid to you shall be made in the discretion
of the Bank's Board of Directors.

          3.   Sign-On Bonus.  You shall receive an initial cash bonus of
               -------------
$100,000 which shall be paid within 30 days of the later of the execution and
delivery of your Employment Agreement with the Bank, dated as of December 2,
1996 (the "Employment Agreement"), and the commencement of your employment with
the Bank.
<PAGE>

                                                                               2

          4.   Long-Term Incentive Opportunity.  During the first two years of
               -------------------------------
the term of your Employment Agreement, to the extent approved, as appropriate,
from time to time by the Compensation Committee or the Board of Directors of the
Bank or the Company, you will be eligible to participate in the Company's Senior
Management Incentive Plan (the "Senior Management Incentive Plan"), with a long-
term incentive in the form of stock options equal in value (as determined by the
Bank) to 60% of your base annual salary.  In the event of the termination of
your employment for any reason (other than for "cause" as defined in the
Employment Agreement), such options shall continue to be exercisable, to the
extent vested, for their full 11-year term as if no such termination had
occurred. To the extent you are granted stock options pursuant to your
participation in the Senior Management Incentive Plan, you will not be entitled
to receive an amount equal to the dividends, if any, that are declared and paid
by the Company on the number of shares for which you hold options that have not
yet lapsed or been exercised unless such dividend equivalents are generally paid
by the Bank to executive officers at a comparable level of responsibility to you
holding stock options.

          5.   Deferred Compensation Plan.  To the extent approved by the
               --------------------------
Compensation Committee of the Bank or the Company, you will be eligible to
participate in the Dime Bancorp, Inc. Voluntary Deferred Compensation Plan.

          6.   Automobile Allowance.  For purposes of enabling you to travel to
               --------------------
and from the Bank's offices and elsewhere for business purposes, the Bank will
provide you during the term of your Employment Agreement with the use of a Bank-
owned or Bank-leased automobile of a make and model commensurate with that being
provided under the Bank's policies as in effect on the date hereof to officers
of the Bank of comparable rank and responsibility, and will reimburse you for
all costs, including tolls and gasoline, incurred by you during such period in
connection with the business operation of the vehicle, subject to the Bank's
policies, as in effect from time to time, concerning personal use of the
automobile.

          7.   Costs of Legal Review.  The Bank will reimburse you promptly upon
               ---------------------
request and the submission of appropriate invoices for the reasonable fees and
disbursements of your counsel incurred in connection with the negotiation,
execution and delivery of your Employment Agreement and this Letter Agreement.

          8.   Dues Reimbursement.  The Bank will reimburse you during the term
               ------------------
of your employment for the reasonable annual (or less frequent) membership fees
for two country, social, business, luncheon or fitness clubs.

          Notwithstanding the foregoing, if any statute, regulation, order,
agreement or regulatory interpretation thereof that is valid and binding upon
the Bank, including, without limitation, 12 USC (S)1828(k) and regulations
thereunder (each a "Regulatory Restriction") restricts, prohibits or limits the
amount of any payment or the provision of any benefit that the Bank would
otherwise be liable for pursuant to this Letter Agreement, then the amount that
the Bank will pay to you will not exceed the maximum amount permissible under
such Regulatory Restriction; provided, that if such Regulatory Restriction shall
subsequently be rescinded, superseded, amended or otherwise determined not to
restrict, limit or prohibit payment by the
<PAGE>

                                                                               3

Bank of amounts otherwise due you hereunder, the Bank shall promptly thereafter
pay to you any amounts (or the value of any benefit) previously withheld from
you as a result of such Regulatory Restriction. The provisions and limitations
set forth in Section 10 of your Employment Agreement, to the extent required by
law, are hereby incorporated by reference herein. Further, if any amount
otherwise payable hereunder other than upon events following a Hostile Change in
Control (as defined in the Employment Agreement) would be deemed to constitute a
parachute payment (a "Parachute Payment") within the meaning of Section 280G of
the Internal Revenue Code of 1986, as amended (the "Code"), and if any such
Parachute Payment, when added to any other payments other than upon events
following a Hostile Change in Control which are deemed to constitute Parachute
Payments, would otherwise result in the imposition of an excise tax under
Section 4999 of the Code, the amounts payable hereunder shall be reduced by the
smallest amount necessary to avoid the imposition of such excise tax. Any such
limitation shall be applied in a manner that considers the benefits that are to
be paid pursuant to the Employment Agreement or otherwise, and such limitation
shall be applied to such compensation and benefit amounts, and in such order, as
the Bank shall determine in its sole discretion. References to the Code
hereunder shall be to the Code as presently in effect or to the corresponding
provisions of any succeeding law.

          This Letter Agreement is intended solely to detail certain of your
initial compensation arrangements with the Bank.  Nothing in this Letter
Agreement (a) confers upon you the right to continue in the employment of the
Bank or the right to hold any particular office or position with the Bank, (b)
requires the Bank to pay you, or entitles you to receive, any specified annual
salary or interferes with or restricts in any way the right of the Bank to
decrease your annual salary at any time, (c) requires the Bank to continue to
provide any of the benefit plans or arrangements described above, or (d)
interferes with or restricts in any way the right of the Bank to terminate your
employment at any time, with or without cause.  In the event of any conflict
between the express provisions of this Letter Agreement and the Employment
Agreement, the express provisions of the Employment Agreement shall be
controlling.

          Any payments due you hereunder shall be reduced by all applicable
withholding and other taxes.

          This Letter Agreement shall be governed by the laws of the State of
New York, without regard to conflict of laws principles applied in the State of
New York.  If any provision of this Letter Agreement is held by a court or other
authority having competent jurisdiction to be invalid, void or otherwise
unenforceable, in whole or in part, by reason of any applicable law, statute or
regulation or any interpretation thereof, then the remainder of the provisions
of this Letter Agreement shall remain in full force and effect and in no way
affected, impaired or invalidated.  This Agreement may be assumed by the Company
at its election.  Following any such election, the obligations of the Bank under
this Agreement shall become the obligations of the Company.  Except as otherwise
provided above, this Letter Agreement may only be amended in writing signed by
both parties hereto.
<PAGE>

                                                                               4

          Please indicate your acceptance to the terms of this Letter Agreement
by signing below.

                         Very truly yours,

                         THE DIME SAVINGS BANK OF NEW YORK, FSB



                         By:  /s/ Lawrence J. Toal
                              -----------------------------------------


AGREED AND ACCEPTED

/s/ Fred B. Koons
---------------------------
Fred B. Koons

Date: 2/27/97