<PAGE>   1
                                                                EXHIBIT 10.2.1


      TAPPAN ZEE FINANCIAL, INC. 1996
              STOCK OPTION PLAN
            FOR OUTSIDE DIRECTORS

         (Adopted on March 25, 1996
       Effective as of July 11, 1996)


                  AMENDMENT


1.   Article II - Effective as of July 11, 1996, Article II shall be amended by
deleting section 2.13 therefrom and redesignating all remaining sections of
Article II and all cross-references thereto accordingly.


2.   Article IV - Effective as of July 11, 1996, section 4.2(b) shall be amended
by substituting the date "July 11, 1997" for the date "October 5, 1996" therein.


3.   Article IV - Effective as of July 11, 1996, Article IV shall be amended by
deleting section 4.7 therefrom.


4.   Article V - Effective as of July 11, 1996, section 5.3 shall be amended and
restated in its entirety to read as follows:

         SECTION 5.3     ADJUSTMENTS IN THE EVENT OF A BUSINESS REORGANIZATION.

                  (a)    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 held by each Person who is
         then a holder of record of Shares, the number of Shares covered by each
         outstanding Option and the number of Shares available pursuant to
         section 4.1 shall be adjusted to account for such event. Such adjust
         ment shall be effected by multiplying such number of Shares by an
         amount equal to the number of Shares that would be owned after such
         event by a Person who, immediately prior to such event, was the holder
         of record of one Share, and the Exercise Price of the Options shall be
         adjusted by dividing the Exercise Price by such number of Shares;
         provided, however, that the Committee may, in its discretion, establish
         another appropriate method of adjustment.

                  (b)    In the event of any merger, consolidation, or other
         business reorganization in which the Company is not the surviving
         entity, any exercisable

                                   Page 1 of 2

<PAGE>   2


         Options granted under the Plan which remain outstanding may be
         cancelled as of the effective date of such merger, consolidation,
         business reorganization, liquidation or sale by the Board upon 30 days'
         written notice to the Option holder; provided, however, that on or as
         soon as practicable following the date of cancellation, each Option
         holder shall receive a monetary payment in such amount, or other
         property of such kind and value, as the Board determines in good faith
         to be equivalent in value to the Options that have been cancelled.

                  (c)    In the event that the Company shall declare and pay any
         dividend with respect to Shares (other than a dividend payable in
         Shares) 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, either:

                           (i)     make an equivalent payment to each Person 
                  holding an outstanding Option as of the record date for such
                  dividend. Such payment shall be made at substantially the same
                  time, in substantially the same form and in substantially the
                  same amount per optioned Share as the dividend or other
                  distribution paid with respect to outstanding Shares;
                  provided, however, that if any dividend or distribution on
                  outstanding Shares is paid in property other than cash, the
                  Company, in the Committee's discretion, may make such payment
                  in a cash amount per optioned Share equal in fair market value
                  to the fair market value of the non-cash dividend or
                  distribution; or

                           (ii)    adjust the Exercise Price of each outstanding
                  Option in such manner as the Committee may determine to be
                  appropriate to equitably reflect the payment of the dividend;
                  or

                           (iii)   take the action described in section 
                  5.3(c)(i) with respect to certain outstanding Options and the
                  action described in section 5.3(c)(ii) 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 this section 5.3(c)
         in a vote taken after October 5, 1996.


5.   Article VI - Effective as of July 11, 1996, section 6.8 shall be amended as
follows: first, the first sentence in such section shall be amended by deleting
therefrom the words "and Limited Stock Appreciation Rights" and second, the
second sentence of section 6.8 shall be amended by deleting therefrom the words
"or Limited Stock Appreciation Rights" each time such words appear therein.

                                   Page 2 of 2