EXHIBIT 4.6.2

                               APPOINTMENT OF
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                      SUCCESSOR ADMINISTRATIVE TRUSTEE
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                                     AND
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                             FIRST AMENDMENT TO
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                    AMENDED AND RESTATED TRUST AGREEMENT
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                                GBB CAPITAL I


          This Appointment of Successor Administrative Trustee and First
Amendment to Amended and Restated Trust Agreement (this "First Amendment"), is
dated as of June 24, 1998 and is pursuant to Sections 8.10, 8.11 and 10.2(a) of
the Amended and Restated Trust Agreement between Greater Bay Bancorp, as
Depositor, Wilmington Trust Company, as Property Trustee, Wilmington Trust
Company, as Delaware Trustee and the Administrative Trustees named therein,
dated as of March 31, 1997 (the "Amended and Restated Trust Agreement").
Capitalized terms used herein and not otherwise defined herein have the
respective meanings ascribed thereto in the Amended and Restated Trust
Agreement.

          WHEREAS, James R. Ramsey, an Administrative Trustee of GBB Capital I
under the Amended and Restated Trust Agreement, has been removed as an
Administrative Trustee by the Common Securityholder pursuant to Section 8.10 of
the Amended and Restated Trust Agreement;

          WHEREAS, Greater Bay Bancorp, as the Common Securityholder, wishes to
appoint a successor Administrative Trustee pursuant to Section 8.10 of the
Amended and Restated Trust Agreement; and

          WHEREAS, Shawn E. Saunders, a natural person over the age of 21, and
the person whom the Common Securityholder wishes to appoint as successor
Administrative Trustee, wishes to accept such appointment pursuant to Section
8.11 of the Amended and Restated Trust Agreement.

          1.   James R. Ramsey, Administrative Trustee under the Amended and
Restated Trust Agreement, is hereby removed as an Administrative Trustee
pursuant to Section 8.10 of the Amended and Restated Trust Agreement by Greater
Bay Bancorp (in its capacity as Common Securityholder).  This First Amendment,
when delivered to the removed Trustee, James R. Ramsey, shall constitute
delivery of the required Act of the Common Securityholder pursuant to Section
8.10 of the Amended and Restated Trust Agreement.

          2.   Greater Bay Bancorp, as Common Securityholder, hereby appoints
Shawn E. Saunders as successor Administrative Trustee.  This First Amendment,
when executed and acknowledged by Shawn E. Saunders, the successor Trustee, and
delivered to GBB Capital I and the removed Administrative Trustee, James R.
Ramsey, shall constitute the instrument accepting such appointment pursuant to
Section 8.11 of the Amended and Restated Trust Agreement.

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          3.   Shawn E. Saunders hereby accepts the appointment under the
Amended and Restated Trust Agreement as successor Administrative Trustee, and
accepts the rights, powers, trusts and duties of an Administrative Trustee with
respect to the Trust Securities and the Trust, as if he were an original
signatory in the capacity as Administrative Trustee (and not in an individual
capacity) to the Amended and Restated Trust Agreement.  This First Amendment
shall constitute the amendment to the Amended and Restated Trust Agreement
required to be executed and delivered by the retiring Trustee and the successor
Trustee pursuant to Section 8.11 of the Amended and Restated Trust Agreement.


                               GENERAL PROVISIONS

     As amended by this First Amendment, the Amended and Restated Trust
Agreement is in all respects ratified and confirmed and, as amended by this
First Amendment, shall be read, taken and construed as one and the same
instrument.

     All other provisions of the Amended and Restated Trust Agreement shall
remain unaffected by the foregoing amendment and shall remain in full force and
effect.
 
     This First Amendment shall become a legally effective and binding
instrument as of the date hereof.

     This First Amendment may be executed in any number of counterparts, each of
which so executed shall be deemed to be an original, but all of such
counterparts shall together constitute one and the same instrument.

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     IN WITNESS WHEREOF, the undersigned have executed this First Amendment as
of the day and year first above written.


                                Greater Bay Bancorp


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


                                Wilmington Trust Company,
                                  as Property Trustee


                                By: /s/ Bruce L. Bisson
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                                    Name:   Bruce L. Bisson
                                    Title:  Vice President


                                    /s/ David L. Kalkbrenner
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                                    David L. Kalkbrenner,
                                     as Administrative Trustee


                                    /s/ Steven C. Smith
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                                    Steven C. Smith,
                                     as Administrative Trustee


                                    /s/ Shawn E. Saunders
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                                    Shawn E. Saunders,
                                     as successor Administrative Trustee



                                    /s/ James R. Ramsey
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                                    James R. Ramsey,
                                     as retiring Administrative Trustee