EXHIBIT 10.11.2

                               AMENDMENT 1998A
                                     TO
                             GREATER BAY BANCORP
                                1997 ELECTIVE
                         DEFERRED COMPENSATION PLAN

          THIS AMENDMENT 1998A TO THE GREATER BAY BANCORP 1997 ELECTIVE DEFERRED
COMPENSATION PLAN ("Amendment 1998A") is made effective as of November 1, 1998,
and is made pursuant to the following recitals:

          A.  Greater Bay Bancorp, a California corporation (the "Company"),
adopted the Greater Bay Bancorp 1997 Elective Deferred Compensation Plan (the
"Plan") at a meeting of the Company's Board of Directors ("Board") on November
19, 1997.  Terms used in this Amendment 1998A have the same meanings as in the
Plan.

          B.  Section 8.01 of the Plan provides rules for amendment of the Plan.

          C.  The Company has determined that it is in the best interests of the
Company and the Subsidiaries (as defined in the Plan) to amend the Plan as set
forth in this Amendment 1998A.

          NOW THEREFORE, in consideration of the foregoing recitals (which are
incorporated herein and made an integral part hereof), the Plan is amended as
follows:

          1.  Section 3.02 of the Plan is amended to read in its entirety as
follows:

          Sections 3.02 Election Procedure.  The Committee shall provide an
                        ------------------                                 
Election Form to each Employee who is selected by the Committee to participate
in the Plan and to become a Participant.  Each such selected eligible Employee
who elects to make a Deferred Compensation Contribution for the applicable Plan
Year shall so specify on the Election Form and shall agree to a corresponding
reduction in his or her cash Compensation.  A Participant must complete his or
her annual Election Form and return it to the Committee on or before such date
as the Committee shall specify.  In the case of a Participant making an election
for the next Plan Year, such date shall be no later than the last day of the
calendar month prior to commencement of the Plan Year for which the
Participant's election shall be effective.  For the initial Plan Year or for an
eligible Employee selected for participation during the course of a Plan Year,
an eligible selected Employee shall elect to participate during the Plan Year in
which he or she first becomes eligible for participation by returning to the
Committee his or her properly completed Election Form on the deferral of
Compensation for services rendered by such Employee after his or her deferral
election.  If such eligible Employee does not make an election during the Plan
Year in which he or she first becomes eligible, a subsequent election may only
be made at the commencement of any succeeding Plan Year.  An election made by an
eligible selected Employee shall apply only for one Plan Year, and each eligible
Employee selected for participation for a subsequent Plan Year must make a
separate election for that Plan Year.

 
          2.  Any corporation that hereafter becomes a Subsidiary and that
adopts the Plan in accordance with Section 9.12 of  the Plan shall automatically
be deemed to have adopted this Amendment 1998A as part of the Plan.

          3.  Except as set forth herein, the Plan shall remain in full force
and effect.

          IN WITNESS WHEREOF, the Company has caused this Amendment 1998A to be
executed in its name and behalf by its officers thereunto duly authorized.


                              GREATER BAY BANCORP,
                              a California corporation



                              By:  /s/ Steven C. Smith
                                  ---------------------------------
                                 Name:   Steven C. Smith
                                 Title:  Executive Vice President,
                                         Chief Operating Officer and
                                         Chief Financial Officer



                       CERTIFICATE OF ASSISTANT SECRETARY

          The undersigned, being duly appointed Assistant Secretary of Greater
Bay Bancorp, a California corporation, hereby certifies that the foregoing
Amendment 1998A was duly adopted by the Board of Directors of such corporation
at a Board meeting on November 17, 1998.



                                 /s/ Steven C. Smith
                                  ---------------------------------
                                  Steven C. Smith
                                  Assistant Secretary