EXHIBIT 4.14

                        SUPPLEMENTAL DEBENTURE AGREEMENT
                        --------------------------------


          THIS SUPPLEMENTAL DEBENTURE AGREEMENT, dated as of March 27, 1997, 
is made pursuant to Article VIII.1 of the Debenture Agreement dated as of
September 27, 1995, as amended by the Supplemental Debenture Agreement dated as
of November 22, 1996 and the Supplemental Debenture Agreement dated as of
November 27, 1996 (the "Debenture Agreement"), pursuant to which Greater Bay
Bancorp, a California corporation ("Greater Bay"), has issued 11.5% Subordinated
Debentures Due 2005 (the "Debentures"). All capitalized terms used herein and
not otherwise defined shall have the meaning given to them in the Debenture
Agreement.


                                    RECITALS

          WHEREAS, Article IV.1 of the Debenture Agreement provides that "the
indebtedness represented by the Debentures and the payment of the principal of
and interest on each and all of the Debentures is hereby expressly subordinated,
to the extent and in the manner hereinafter set forth, in right of payment to
the prior payment in full of all Senior Indebtedness."

          WHEREAS, Article I.1 of the Debenture Agreement provides that Senior
Indebtedness means "the principal of, premium, if any, and interest on, and any
other payment due pursuant to any of the following whether outstanding on the
date hereof or thereafter created, assumed or incurred:  (1) all indebtedness of
the Company for money borrowed (including indebtedness of others guaranteed by
the Company and other direct credit substitutes) other than the Debentures, (2)
any indebtedness or obligation of the Company as to which it is expressly
provided that such indebtedness or obligation is senior to the Debentures, (3)
any amendments, renewals, extensions, deferrals, modifications and refundings of
any such indebtedness described in subsection (1) or (2) above, unless in either
case in the instrument creating or evidencing any such indebtedness or pursuant
to which it is outstanding it is expressly provided that such indebtedness is
not superior in right of payment to the Debentures, and (4) Derivative
Obligations."

          WHEREAS, Greater Bay anticipates entering into a Junior Subordinated
Indenture between Greater Bay and Wilmington Trust Company, as Trustee  (the
"Indenture") pursuant to which Greater Bay will issue 9.75% Junior Subordinated
Deferrable Interest Debentures Due April 1, 2027 (the "Junior Subordinated
Debentures").

          WHEREAS, Section 13.1 of the Indenture provides that payment of the
principal of (and premium, if any) and interest on each and all of the Junior
Subordinated Debentures is "subordinate and subject in right of payment to the
prior payment in full of all amounts then due and payable in respect of all
Senior and Subordinated Debt."

          WHEREAS, Section 1.1 of the Indenture provides that "Senior and
Subordinated Debt shall be deemed to include the 11.5% Subordinated Debentures
Due 2005 of the Company."

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          WHEREAS, Article VIII.1 of the Debenture Agreement provides that
Greater Bay may, when authorized by a Board Resolution, enter into a
Supplemental Debenture Agreement for the purpose of curing any ambiguity or
making any other provision with respect to matters or questions arising under
the Debenture Agreement which shall not adversely affect the interests of the
Holders of Debentures in any material respect.

          WHEREAS, on March 27, 1997 the Board of Directors of Greater Bay
authorized the amendment of the Debenture Agreement to clarify that,
notwithstanding the definition of Senior Indebtedness contained in Article I.1
of the Debenture Agreement, the Junior Subordinated Debentures shall not
constitute Senior Indebtedness within the meaning of the Debenture Agreement.

          WHEREAS, Greater Bay desires to amend the Debenture Agreement to
reflect that, notwithstanding the definition of Senior Indebtedness contained in
Article I.1 of the Debenture Agreement, the Junior Subordinated Debentures shall
not constitute Senior Indebtedness within the meaning of the Debenture
Agreement.
 

                                   AMENDMENT

          NOW, THEREFORE, Greater Bay hereby amends the Debenture Agreement to
reflect that, notwithstanding the definition of Senior Indebtedness contained in
Article I.1 of the Debenture Agreement, the Junior Subordinated Debentures shall
not constitute Senior Indebtedness within the meaning of the Debenture
Agreement.


                               GENERAL PROVISIONS

          As amended by this Supplemental Debenture Agreement, the Debenture
Agreement is in all respects ratified and confirmed and, as amended by this
Supplemental Debenture Agreement, shall be read, taken and construed as one and
the same instrument.
 
          This Supplemental Debenture Agreement shall become a legally effective
and binding instrument as of the date hereof.

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          IN WITNESS WHEREOF, Greater Bay has caused this Supplemental Debenture
Agreement to be duly signed and acknowledged by its officers all as of the day
and year first above written.

                              GREATER BAY BANCORP


                              By: /s/ David L. Kalkbrenner
                                  ------------------------------------
                                  David L. Kalkbrenner, President and
                                  Chief Executive Officer
 

Attest:

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

 

 

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