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                                  Exhibit 4.2

                         REGISTRATION RIGHTS AGREEMENT

     This REGISTRATION RIGHTS AGREEMENT, dated as of March 23, 2000 (this

"Agreement"), is made by and among Greater Bay Bancorp., a California
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corporation (the "Company"), and the investors named on the signature pages
                  -------
hereto (the "Initial Investors").
             -----------------

                                   RECITALS:

     A.  In connection with the Securities Purchase Agreement dated March 22,
2000 between the Initial Investors and the Company (the "Purchase Agreement"),
                                                         ------------------
the Company has agreed, upon the terms and subject to the conditions of the
Purchase Agreement, to issue and sell to the Initial Investors 324,324 shares of
the Company's Common Stock (the "Common Shares").
                                 -------------

     B.  In order to induce the Initial Investors to execute and deliver the
Purchase Agreement, the Company has agreed to provide certain registration
rights under the Securities Act and applicable state securities laws with
respect to the Common Shares.

     In consideration of the premises and the mutual covenants contained herein
and other good and valuable consideration, the receipt and sufficiency of which
are hereby acknowledged, the Company and the Initial Investors hereby agree as
follows:

                                   ARTCILE 1
                                  DEFINITIONS

     Capitalized terms used and not otherwise defined herein have the respective
meanings given them set forth in the Purchase Agreement.  In addition, as used
in this Agreement, the following terms have the following meanings:

     1.1  "Common Shares" means the shares of Common Stock sold pursuant to the
           -------------
Purchase Agreement.

     1.2 "Investors" means the Initial Investors and any of their transferees or
          ---------
assignees who agree to become bound by the provisions of this Agreement in
accordance with Article IX hereof.

     1.3  "Registrable Securities" means the Common Shares sold pursuant to the
           ----------------------
Purchase Agreement and any shares of capital stock issued or issuable from time
to time (with any adjustments) in exchange for or otherwise with respect to the
Common Shares.

     1.4 "Registration Period" means the period between the date of this
          -------------------
Agreement and the earlier of (i) the date on which all of the Registrable
Securities have been sold and no further Registrable Securities may be issued in
the future, (ii) the date on which all the Registrable Securities (in the
opinion of the Investors' counsel) may be immediately sold without registration
and without limitation as to volume by each holder thereof as to the number of
Registrable

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Securities to be sold, pursuant to Rule 144 or otherwise, or (iii) the second
anniversary of the date of this Agreement.

     1.5  "Registration Statement" means a Registration Statement of the Company
           ----------------------
filed under the Securities Act.

     1.6  The terms "register," "registered," and "registration" refer to a
                     --------    ----------        ------------
registration effected by preparing and filing a Registration Statement or
statements in compliance with the Securities Act and pursuant to Rule 415 and
the declaration or ordering of effectiveness of such Registration Statement by
the SEC.

     1.7 "Rule 415" means Rule 415 under the Securities Act, or any successor
          --------
Rule providing for offering securities on a continuous basis, and applicable
rules and regulations thereunder.

                                  ARTICLE II
                                  REGISTRATION

     2.1 Mandatory Registration. The Company will use its commercially
         ----------------------
reasonable efforts to file with the SEC a Registration Statement on Form S-3
registering the Registrable Securities and no other securities for resale within
30 business days after the Closing Date of the purchase of the Common Shares
under the Purchase Agreement. If Form S-3 is not available at that time, then
the Company will file a Registration Statement on such form as is then available
to effect a registration of the Registrable Securities, subject to the consent
of the Initial Investors, which consent will not be unreasonably withheld.

     2.2  Effectiveness of the Registration Statement.  The Company will use its
          -------------------------------------------
commercially reasonable efforts to cause the Registration Statement to be
declared effective by the SEC as soon as practicable after filing, and in any
event no later than the 90th day after the Closing Date (the "Required Effective
                                                              ------------------
Date").  However, so long as the Company filed the Registration Statement within
----
30 business days after the Closing Date, if the Registration Statement receives
SEC review, then the Required Effective Date will be the 120th day after the
Closing Date.  The Company's commercially reasonable efforts will include, but
not be limited to, promptly responding to all comments received from the staff
of the SEC.  If the Company receives notification from the SEC that the
Registration Statement will receive no action or review from the SEC, then the
Company will, subject to its rights under Section 3.5, cause the Registration
Statement to become effective within five business days after such SEC
notification.  Once the Registration Statement is declared effective by the SEC,
the Company will use its commercially reasonable efforts to cause the
Registration Statement to remain effective throughout the Registration Period,
subject to the Company's rights under Section 3.5.

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     2.3  Piggyback Registrations.
     -----------------------------

        (a) If, at any time prior to the expiration of the Registration Period,
a Registration Statement is not effective with respect to all of the Registrable
Securities and the Company decides to register any of its Common Stock for its
own account or for the account of others, then the Company will promptly give
the Investors written notice thereof and will use its commercially reasonable
efforts to include in such registration all or any part of the Registrable
Securities requested by such Investors to be included therein (excluding any
Registrable Securities previously included in a Registration Statement). This
requirement does not apply to Company registrations on Form S-3, Form S-4 or
Form S-8 or their equivalents relating to (i) Common Stock to be issued solely
in connection with a dividend reinvestment plan or an acquisition of any entity
or business or (ii) Common Stock issuable in connection with stock option or
other employee benefit plans. Each Investor must give its request for
registration under this paragraph to the Company in writing within 15 days after
receipt from the Company of notice of such pending registration. If the
registration for which the Company gives notice is a public offering involving
an underwriting, the Company will so advise the Investors as part of the above-
described written notice. In that event, if the managing underwriter(s) of the
public offering impose a limitation on the number of shares of Common Stock that
may be included in the Registration Statement because, in such underwriter(s)'
judgment, such limitation would be necessary to effect an orderly public
distribution, then the Company will be obligated to include only such limited
portion, if any, of the Registrable Securities with respect to which such
Investors have requested inclusion hereunder. Any exclusion of Registrable
Securities will be made pro rata among all holders of the Company's securities
seeking to include shares of Common Stock in proportion to the number of shares
of Common Stock sought to be included by those holders. However, the Company
will not exclude any Registrable Securities unless the Company has first
excluded all outstanding securities the holders of which are not entitled by
right to inclusion of securities in such Registration Statement or are not
entitled pro rata inclusion with the Registrable Securities. No Investor may
participate in any distribution of Common Stock under this Section 2.4 unless
such Investor (i) agrees to sell such Investor's Registrable Securities on the
basis provided in any underwriting arrangements or other plan of distribution
approved by the Company in its sole discretion, (ii) completes and executes all
questionnaires, powers of attorney, indemnities, underwriting agreements and
other documents reasonably required under the terms of such underwriting
arrangements or other plan of distribution, and (iii) agrees to pay its pro rata
share of all underwriting discounts and commissions and other fees and expenses
of investment bankers and any manager or managers of such underwriting, and
legal expenses of the underwriter, applicable with respect to its Registrable
Securities, in each case to the extent not payable by the Company under the
terms of this Agreement.

        (b) No right to registration of Registrable Securities under this
Section 2.3 limits in any way the registration required under Section 2.1 above.
The obligations of the Company under this Section 2.3 expire upon the earlier of
(i) the effectiveness of the Registration Statement filed pursuant to Section
2.1 above, (ii) after the Company has afforded the opportunity for the Investors
to exercise registration rights under this Section 2.3 for two registrations
(provided, however, that any Investor that has had any Registrable Securities
excluded from any Registration Statement in accordance with this Section 2.3 may
include in any additional Registration Statement filed by the Company the
Registrable Securities so excluded), (iii) when all of the Registrable
Securities held by any Investor may be sold by such Investor under Rule 144

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without being subject to any volume restrictions, or (iv) the second anniversary
of the date of this Agreement.

     2.4 Eligibility to use Form S-3. The Company represents and warrants that
         ---------------------------
it meets the requirements for the use of Form S-3 for registration of the sale
by the Investors of the Registrable Securities. The Company will use its
commercially reasonable efforts to file all reports required to be filed by the
Company with the SEC in a timely manner so as to preserve its eligibility for
the use of Form S-3.

                                  ARTICLE III
                     ADDITIONAL OBLIGATIONS OF THE COMPANY

     3.1  Continued Effectiveness of Registration Statement.  Subject to the
          -------------------------------------------------
Company's rights under Section 3.5, the Company will keep the Registration
Statement covering the Registrable Securities effective under Rule 415 at all
times during the Registration Period.

     3.2 Accuracy of Registration Statement. Subject to the Company's rights
         ----------------------------------
under Section 3.5, any Registration Statement (including any amendments or
supplements thereto and prospectuses contained therein) filed by the Company
covering Registrable Securities will not contain any untrue statement of a
material fact or omit to state a material fact required to be stated therein, or
necessary to make the statements therein, in light of the circumstances in which
they were made, not misleading. Subject to the limitations set forth in Section
3.5, the Company will prepare and file with the SEC such amendments (including
post-effective amendments) and supplements to the Registration Statement and the
prospectus used in connection with the Registration Statement as may be
necessary to permit sales pursuant to the Registration Statement at all times
during the Registration Period, and, during such period, will comply with the
provisions of the Securities Act with respect to the disposition of all
Registrable Securities of the Company covered by the Registration Statement
until the termination of the Registration Period, or if earlier, until such time
as all of such Registrable Securities have been disposed of in accordance with
the intended methods of disposition by the seller or sellers thereof as set
forth in the Registration Statement.

     3.3 Furnishing Documentation. The Company will furnish to each Investor
         ----------------------------------
whose Registrable Securities are included in a Registration Statement, and to
its legal counsel, (a) promptly after each document is prepared and publicly
distributed, filed with the SEC or received by the Company, one copy of any
Registration Statement filed pursuant to this Agreement and any amendments
thereto, each preliminary prospectus and final prospectus and each amendment or
supplement thereto; and, in the case of a Registration Statement filed under
Section 2.1 above, each letter written by or on behalf of the Company to the SEC
and each item of correspondence from the SEC or the staff of the SEC, in each
case relating to such Registration Statement (other than any portion of any item
thereof which contains information for which the Company has sought confidential
treatment); and (b) a number of copies of a prospectus, including a preliminary
prospectus, and all amendments and supplements thereto, and such other documents
as the Investor may reasonably request in order to facilitate the disposition of
the Registrable Securities owned by the Investor. The Company will immediately
notify by facsimile each Investor whose Registrable Securities are included in
any Registration Statement of the effectiveness of the Registration Statement
and any post-effective amendment.

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<PAGE>

     3.4 Additional Obligations. The Company will use its commercially
         ----------------------
reasonable efforts to (a) register and qualify the Registrable Securities
covered by a Registration Statement under such other securities or blue sky laws
of such jurisdictions as each Investor who holds (or has the right to hold)
Registrable Securities being offered reasonably requests, (b) prepare and file
in those jurisdictions any amendments (including post-effective amendments) and
supplements to such registrations and qualifications as may be necessary to
maintain their effectiveness during the Registration Period, (c) take any other
actions necessary to maintain such registrations and qualifications in effect at
all times during the Registration Period, and (d) take any other actions
reasonably necessary or advisable to qualify the Registrable Securities for sale
in such jurisdictions. Notwithstanding the foregoing, the Company is not
required, in connection with such obligations, to (i) qualify to do business in
any jurisdiction where it would not otherwise be required to qualify but for
this Section 3.4, (ii) subject itself to general taxation in any such
jurisdiction, (iii) file a general consent to service of process in any such
jurisdiction, (iv) provide any undertakings that cause material expense or
burden to the Company, or (v) make any change in its articles of incorporation
or bylaws, which in each case the Board of Directors of the Company determines
to be contrary to the best interests of the Company and its shareholders.

     3.5 Suspension of Registration.
         --------------------------

         (a) The Company will notify (by telephone or electronic mail and also
by facsimile or reputable overnight courier) each Investor who holds Registrable
Securities being sold pursuant to a Registration Statement of the happening of
any event of which the Company has knowledge as a result of which the prospectus
included in the Registration Statement as then in effect includes an untrue
statement of a material fact or omits to state a material fact required to be
stated therein or necessary to make the statements therein, in light of the
circumstances under which they were made, not misleading. The Company will make
such notification as promptly as practicable after the Company becomes aware of
the event (but in no event, without the prior written consent of the Investor,
will the Company disclose to any Investor any of the facts or circumstances
regarding the event), will promptly (but in no event more than 15 business days)
prepare a supplement or amendment to the Registration Statement to correct such
untrue statement or omission, and will deliver a number of copies of such
supplement or amendment to each Investor as such Investor may reasonably
request.

         (b) Notwithstanding anything to the contrary contained in this
Agreement, if in the good faith judgment of the Company resales of Registrable
Securities made pursuant to the Registration Statement might require disclosure
of material information that (i) might interfere with or affect any financing,
acquisition, or other significant transaction being contemplated by the Company,
whether or not a final determination has been made to undertake such
transaction, or (ii) the Company has a bona fide business purpose for preserving
as confidential, and, with respect to each of (i) and (ii) that the Company is
not otherwise required by applicable securities laws or regulations to disclose,
the Company will have the right to delay the effectiveness of the Registration
Statement or suspend the use of the Registration Statement for a period of not
more than 30 consecutive days and for no more than 120 days in the aggregate
during any twelve month period; provided, however, such 30 day period may upon
notice to the Investors be extended for up to an additional 30 days if such
additional time is reasonably necessary to complete financial statements or
reports or other disclosure materials reasonably necessary to be disclosed in
the Registration Statement.

                                       5
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         (c) Subject to the Company's rights under this Section 3, the Company
will use its commercially reasonable efforts to prevent the issuance of any stop
order or other suspension of effectiveness of a Registration Statement and, if
such an order is issued, will use its commercially reasonable efforts to obtain
the withdrawal of such order at the earliest possible time and to notify each
Investor that holds Registrable Securities being sold of the issuance of such
order and the resolution thereof.

         (d) If the use of the Registration Statement is suspended by the
Company, the Company will promptly give notice of the suspension to all
Investors whose securities are covered by the Registration Statement, and will
promptly notify each such Investor as soon as the use of the Registration
Statement may be resumed.

     3.6 Review by the Investors. The Company will permit a single firm of legal
         -----------------------
counsel, designated by the Investors who hold a majority in interest of the
Registrable Securities being sold pursuant to a Registration Statement, to
review the Registration Statement and all amendments and supplements thereto (as
well as all requests for acceleration or effectiveness thereof) a reasonable
period of time prior to their filing with the SEC, and will not file any
document in a form to which such counsel reasonably objects, unless otherwise
required by law in the opinion of the Company's counsel. The sections of any
such Registration Statement including information with respect to the Investors,
the Investors' beneficial ownership of securities of the Company or the
Investors' intended method of disposition of Registrable Securities must conform
to the information provided to the Company by each of the Investors.

     3.7 Information. The Company will make generally available to its security
         -----------
holders as soon as practicable, but not later than 90 days after the close of
the period covered thereby, an earnings statement (in a form complying with the
provisions of Rule 158 under the Securities Act) covering a 12-month period
beginning not later than the first day of the Company's fiscal quarter next
following the effective date of the Registration Statement.

     3.8 Due Diligence; Confidentiality.
         ------------------------------
         (a) The Company will make available for inspection by any Investor
whose Registrable Securities are being sold pursuant to a Registration Statement
and one firm of attorneys retained by the Investors (collectively, the
"Inspectors"), all pertinent financial and other records, pertinent corporate
 ----------
documents and properties of the Company (collectively, the "Records"), as each
                                                            -------
Inspector reasonably deems necessary to enable the Inspector to exercise its due
diligence responsibility. The Company will cause its officers, directors and
employees to supply all information that any Inspector may reasonably request
for purposes of performing such due diligence.

         (b) Each Inspector will hold in confidence, and will not make any
disclosure (except to an Investor) of, any Records or other information that the
Company determines in good faith to be confidential, and of which determination
the Inspectors are so notified, unless (i) the disclosure of such Records is
necessary to avoid or correct a misstatement or omission in any Registration
Statement, (ii) the release of such Records is ordered pursuant to a subpoena or
other order from a court or government body of competent jurisdiction, or (iii)
the information in such Records has been made generally available to the public
other than by disclosure in violation of

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this or any other agreement. The Company is not required to disclose any
confidential information in the Records to any Inspector unless and until such
Inspector has entered into a confidentiality agreement (in form and substance
satisfactory to the Company) with the Company with respect thereto,
substantially in the form of this Section 3.8. Each Investor will, upon learning
that disclosure of Records containing confidential information is sought in or
by a court or governmental body of competent jurisdiction or through other
means, give prompt notice to the Company and allow the Company, at the Company's
expense, to undertake appropriate action to prevent disclosure of, or to obtain
a protective order for, the Records deemed confidential. Nothing herein will be
deemed to limit the Investor's ability to sell Registrable Securities in a
manner that is otherwise consistent with applicable laws and regulations.

         (c) The Company will hold in confidence, and will not make any
disclosure of, information concerning an Investor provided to the Company under
this Agreement unless (i) disclosure of such information is necessary to comply
with federal or state securities laws, (ii) the disclosure of such information
is necessary to avoid or correct a misstatement or omission in any Registration
Statement, (iii) the release of such information is ordered pursuant to a
subpoena or other order from a court or governmental body of competent
jurisdiction, (iv) such information has been made generally available to the
public other than by disclosure in violation of this Agreement or any other
agreement, or (v) such Investor consents to the form and content of any such
disclosure. If the Company learns that disclosure of such information concerning
an Investor is sought in or by a court or governmental body of competent
jurisdiction or through other means, the Company will give prompt notice to such
Investor prior to making such disclosure and allow such Investor, at its
expense, to undertake appropriate action to prevent disclosure of, or to obtain
a protective order for, such information.

     3.9 Listing. The Company will use its commercially reasonable efforts (i)
         -------
to cause all of the Registrable Securities covered by each Registration
Statement to be listed on each national securities exchange on which securities
of the same class or series issued by the Company are then listed, if any, if
the listing of such Registrable Securities is then permitted under the rules of
such exchange, or (ii) to the extent the securities of the same class or series
are not then listed on a national securities exchange, to secure the designation
and quotation of all of the Registrable Securities covered by each Registration
Statement on Nasdaq and, without limiting the generality of the foregoing,
arrange for at least two market makers to register with the National Association
of Securities Dealers, Inc. as such with respect to such Registrable Securities.

     3.10 Transfer Agent; Registrar. The Company will provide a transfer agent
          -------------------------
and registrar, which may be a single entity, for the Registrable Securities not
later than the effective date of the Registration Statement.

     3.11 Share Certificates. The Company will cooperate with the Investors who
          ------------------
hold Registrable Securities being sold to facilitate the timely preparation and
delivery of certificates (not bearing any restrictive legends) representing
Registrable Securities to be offered pursuant to a Registration Statement and
will enable such certificates to be in such denominations or amounts as the case
may be, and registered in such names as the Investors may reasonably request,
all in accordance with Article V of the Purchase Agreement.

                                       7
<PAGE>

     3.12 Plan of Distribution. At the request of the Investors holding a
          --------------------
majority in interest of the Registrable Securities registered pursuant to a
Registration Statement, the Company will promptly prepare and file with the SEC
such amendments (including post-effective amendments) and supplements to the
Registration Statement, and the prospectus used in connection with the
Registration Statement, as may be necessary in order to change the plan of
distribution set forth in such Registration Statement. Notwithstanding the
foregoing, each Investor agrees that the Investors may not change the plan of
distribution to involve an underwritten offering.

     3.13 Securities Laws Compliance. The Company will comply with all
          --------------------------
applicable laws related to any Registration Statement relating to the sale of
Registrable Securities and to offering and sale of securities and with all
applicable rules and regulations of governmental authorities in connection
therewith (including, without limitation, the Securities Act, the Exchange Act
and the rules and regulations promulgated by the SEC).

     3.14 Further Assurances.  Subject to the limitations set forth in the last
          ------------------
sentence of Section 3.12, the Company will take all other reasonable actions as
any Investor may reasonably request to expedite and facilitate disposition by
such Investor of the Registrable Securities pursuant to the Registration
Statement.

     3.15 No Additional Selling Shareholders. The Company will not, and will not
          ----------------------------------
agree to, allow the holders of any securities of the Company to include any of
their securities in any Registration Statement under Section 2.1 hereof, or any
amendment or supplement thereto under Section 3.2 hereof, without the consent of
the holders of a majority in interest of the Registrable Securities.

                                  ARTICLE IV
                          OBLIGATIONS OF THE INVESTORS

     4.1 Investor Information. As a condition to the obligations of the Company
         --------------------
to complete any registration pursuant to this Agreement with respect to the
Registrable Securities of each Investor, such Investor will furnish to the
Company such information regarding itself, the Registrable Securities held by it
and the intended method of disposition of the Registrable Securities held by it
as is reasonably required by the Company to effect the registration of the
Registrable Securities. At least five (5) business days prior to the first
anticipated filing date of a Registration Statement for any registration under
this Agreement, the Company will notify each Investor of the information the
Company requires from that Investor if the Investor elects to have any of its
Registrable Securities included in the Registration Statement. If, within three
business days prior to the filing date, the Company has not received the
requested information from an Investor, then the Company may file the
Registration Statement without including Registrable Securities of that
Investor.

     4.2 Further Assurances. Each Investor will cooperate with the Company, as
         ------------------
reasonably requested by the Company, in connection with the preparation and
filing of any Registration Statement hereunder, unless such Investor has
notified the Company in writing of such Investor's election to exclude all of
such Investor's Registrable Securities from the Registration Statement.

                                       8
<PAGE>

     4.3 Suspension of Transactions. Upon receipt of any notice from the Company
         --------------------------
of the happening of any event of the kind described in Section 3.5, each
Investor agrees that it (a) will immediately discontinue disposition of
Registrable Securities pursuant to the Registration Statement covering such
Registrable Securities (b) will not disclose to any other person that its use of
the Registration Statement has been suspended and (c) will not, either directly
or indirectly, engage in any transaction involving any of the securities of the
Company, until with respect to each of (a), (b) and (c), it receives copies of
the supplemented or amended prospectus contemplated by Section 3.5 or is
otherwise notified by the Company that the use of the Registration Statement may
be resumed. If so directed by the Company, each Investor will deliver to the
Company (at the expense of the Company) or destroy (and deliver to the Company a
certificate of destruction) all copies in the Investor's possession (other than
a limited number of file copies) of the prospectus covering such Registrable
Securities that is current at the time of receipt of such notice.

                                   ARTICLE V
                            EXPENSES OF REGISTRATION

     The Company will bear all reasonable expenses, other than underwriting
discounts and commissions, and transfer taxes, if any, incurred in connection
with registrations, filings or qualifications pursuant to Article II of this
Agreement, including, without limitation, all registration, listing and
qualifications fees, printers and accounting fees, the fees and disbursements of
counsel for the Company, and the reasonable fees and disbursements of one firm
of legal counsel selected by the Initial Investors pursuant to Section 3.6
hereof.

                                  ARTICLE VI
                                INDEMNIFICATION

     In the event that any Registrable Securities are included in a Registration
Statement under this Agreement:

     6.1  To the extent permitted by law, the Company will indemnify and hold
harmless each Investor that holds such Registrable Securities, any directors or
officers of such Investor and any person who controls such Investor within the
meaning of the Securities Act or the Exchange Act (each, an "Indemnified
                                                             -----------
Person") against any losses, claims, damages, expenses or liabilities (joint or
------
several) (collectively, and together with actions, proceedings or inquiries by
any regulatory or self-regulatory organization, whether commenced or threatened
in respect thereof, "Claims") to which any of them become subject under the
                     ------
Securities Act, the Exchange Act or otherwise, insofar as such Claims arise out
of or are based upon any of the following statements, omissions or violations in
a Registration Statement filed pursuant to this Agreement, any post-effective
amendment thereof or any prospectus included therein:  (a) any untrue statement
or alleged untrue statement of a material fact contained in the Registration
Statement or any post-effective amendment thereof or the omission or alleged
omission to state therein a material fact required to be stated therein or
necessary to make the statements therein not misleading, (b) any untrue
statement or alleged untrue statement of a material fact contained in the
prospectus (as it may be amended or supplemented) or the omission or alleged
omission to state therein any material fact necessary to make the statements
made therein, in light of the circumstances under which the statements therein
were made, not misleading, or (c) any violation or alleged violation

                                       9
<PAGE>

by the Company of the Securities Act, the Exchange Act or any other law,
including without limitation any state securities law or any rule or regulation
thereunder (the matters in the foregoing clauses (a) through (c) being,
collectively, "Violations"). Subject to the restrictions set forth in Section
               ----------
6.3 with respect to the number of legal counsel, the Company will reimburse the
Investors and each such other Indemnified Person, promptly as such expenses are
incurred and are due and payable, for any legal fees or other reasonable
expenses incurred by them in connection with investigating or defending any
Claim. Notwithstanding anything to the contrary contained herein, the
indemnification agreement contained in this Section 6.1 (i) does not apply to a
Claim arising out of or based upon a Violation that occurs in reliance upon and
in conformity with information furnished in writing to the Company by any
Indemnified Person expressly for use in connection with the preparation of the
Registration Statement or any such amendment thereof or supplement thereto, (ii)
does not apply to amounts paid in settlement of any Claim if such settlement is
made without the prior written consent of the Company, which consent will not be
unreasonably withheld, and (iii) with respect to any prospectus, does not apply
and shall not inure to the benefit of any Indemnified Person if the untrue
statement or omission of material fact contained in such prospectus was
corrected on a timely basis and the prospectus, as then amended or supplemented,
if such corrected prospectus was timely made available by the Company pursuant
to Section 3.3 hereof, and the Indemnified Person was promptly advised in
writing not to use the incorrect prospectus prior to the use giving rise to a
Violation and such Indemnified Person, notwithstanding such advice, used it.
This indemnity obligation will remain in full force and effect regardless of any
investigation made by or on behalf of the Indemnified Persons and will survive
the transfer of the Registrable Securities by the Investors under Article IX of
this Agreement.

     6.2  In connection with any Registration Statement in which an Investor is
participating, each such Investor will indemnify and hold harmless, to the same
extent and in the same manner set forth in Section 6.1 above, the Company, each
of its directors, each of its officers who signs the Registration Statement,
each person, if any, who controls the Company within the meaning of the
Securities Act or the Exchange Act, and any other Shareholder selling securities
pursuant to the Registration Statement or any of its directors or officers or
any person who controls such Shareholder within the meaning of the Securities
Act or the Exchange Act (each an "Indemnified Person") against any Claim to
                                  ------------------
which any of them may become subject under the Securities Act, the Exchange Act
or otherwise, insofar as such Claim arises out of or is based upon any
Violation, in each case to the extent (and only to the extent) that such
Violation occurs in reliance upon and in conformity with written information
furnished to the Company by such Investor expressly for use in connection with
such Registration Statement.  Subject to the restrictions set forth in Section
6.3, such Investor will promptly reimburse any legal or other expenses (promptly
as such expenses are incurred and due and payable) reasonably incurred by them
in connection with investigating or defending any such Claim.  However, the
indemnity agreement contained in this Section 6.2 does not apply to amounts paid
in settlement of any Claim if such settlement is effected without the prior
written consent of such Investor, which consent will not be unreasonably
withheld, and no Investor will be liable under this Agreement (including this
Section 6.2 and Article VII) for the amount of any Claim that exceeds the net
proceeds actually received by such Investor as a result of the sale of
Registrable Securities pursuant to such Registration Statement.  This indemnity
will remain in full force and effect regardless of any investigation made by or
on behalf of an Indemnified Party and will survive the transfer of the
Registrable Securities by the Investors under Article IX of this Agreement.
Notwithstanding anything to the contrary contained herein, the

                                       10
<PAGE>

Indemnification Agreement contained in this Section 6.2 with respect to any
prospectus does not apply to and shall not inure to the benefit of any
Indemnified Party if the untrue statement or omission of material fact by the
Investor contained in the prospectus was corrected on a timely basis and the
prospectus, as then amended or supplemented, and the Indemnified Party failed to
utilize such corrected prospectus.

     6.3 Promptly after receipt by an Indemnified Person under this Article VI
of notice of the commencement of any action (including any governmental action),
such Indemnified Person will, if a Claim in respect thereof is to be made
against any indemnifying party under this Article VI, deliver to the
indemnifying party a written notice of the commencement thereof. The
indemnifying party may participate in, and, to the extent the indemnifying party
so desires, jointly with any other indemnifying party similarly given notice,
assume control of the defense thereof with counsel mutually satisfactory to the
indemnifying parties and the Indemnified Person. In that case, the indemnifying
party will diligently pursue such defense. If, in the reasonable opinion of
counsel retained by the indemnifying party, the representation by such counsel
of the Indemnified Person and the indemnifying party would be inappropriate due
to actual or potential conflicts of interest between the Indemnified Person and
any other party represented by such counsel in such proceeding or the actual or
potential defendants in, or targets of, any such action including the
Indemnified Person, and any such Indemnified Person reasonably determines that
there may be legal defenses available to such Indemnified Person that are
different from or in addition to those available to the indemnifying party, then
the Indemnified Person is entitled to assume such defense and may retain its own
counsel, with the fees and expenses to be paid by the indemnifying party. The
Company will pay for only one separate legal counsel for the Investors
collectively, and such legal counsel will be selected by the Investors holding a
majority in interest of the Registrable Securities. The failure to deliver
written notice to the indemnifying party within a reasonable time of the
commencement of any such action does not relieve an indemnifying party of any
liability to an Indemnified Person under this Article 6, except to the extent
that the indemnifying party is prejudiced in its ability to defend such action.
The indemnification required by this Article 6 will be made by periodic payments
of the amount thereof during the course of the investigation or defense, as such
expense, loss, damage or liability is incurred and is due and payable.

                                  ARTICLE VII
                                  CONTRIBUTION

     To the extent that any indemnification provided for herein is prohibited or
limited by law, the indemnifying party will make the maximum contribution with
respect to any amounts for which it would otherwise be liable under Article 6 to
the fullest extent permitted by law.   However, (a) no contribution will be made
under circumstances where the maker would not have been liable for
indemnification under the fault standards set forth in Article 6, (b) no seller
of Registrable Securities guilty of fraudulent misrepresentation (within the
meaning of Section 11(f) of the Securities Act) will be entitled to contribution
from any seller of Registrable Securities who was not guilty of such fraudulent
misrepresentation, and (c) contribution (together with any indemnification or
other obligations under this Agreement) by any seller of Registrable Securities
will be limited in amount to the net amount of proceeds received by such seller
from the sale of such Registrable Securities.

                                       11
<PAGE>

                                 ARTICLE VIII
                             EXCHANGE ACT REPORTING

     In order to make available to the Investors the benefits of Rule 144 or any
similar rule or regulation of the SEC that may at any time permit the Investors
to sell securities of the Company to the public without registration, the
Company will use it commercially reasonable efforts to:

        (a) File with the SEC in a timely manner, and make and keep available,
all reports and other documents required of the Company under the Securities Act
and the Exchange Act so long as the Company remains subject to such requirements
(it being understood that nothing herein limits the Company's obligations under
Section 4.3 of the Purchase Agreement) and the filing and availability of such
reports and other documents is required for the applicable provisions of Rule
144; and

        (b) Furnish to each Investor, so long as such Investor holds Registrable
Securities, promptly upon the Investor's request, (i) a written statement by the
Company that it has complied with the reporting requirements of Rule 144, the
Securities Act and the Exchange Act, (ii) a copy of the most recent annual or
quarterly report of the Company and such other reports and documents filed by
the Company with the SEC and (iii) such other information as may be reasonably
requested to permit the Investors to sell such securities pursuant to Rule 144
without registration.

                                  ARTICLE IX
                       ASSIGNMENT OF REGISTRATION RIGHTS

     The rights of the Investors hereunder, including the right to have the
Company register Registrable Securities pursuant to this Agreement, will be
automatically assigned by the Investors to transferees or assignees of all or
any portion of the Registrable Securities, but only if (a) the Investor agrees
in writing with the transferee or assignee to assign such rights, and a copy of
such agreement is furnished to the Company within a reasonable time after such
assignment, (b) the Company is, within a reasonable time after such transfer or
assignment, furnished with written notice of the name and address of such
transferee or assignee and the securities with respect to which such
registration rights are being transferred or assigned, (c) after such transfer
or assignment, the further disposition of such securities by the transferee or
assignee is restricted under the Securities Act and applicable state securities
laws, (d) at or before the time the Company received the written notice
contemplated by clause (b) of this sentence, the transferee or assignee agrees
in writing with the Company to be bound by all of the provisions contained
herein, (e) such transfer is made in accordance with the applicable requirements
of the Purchase Agreement, and (f) the transferee is an "accredited investor" as
that term is defined in Rule 501 of Regulation D.

                                   ARTICLE X
                        AMENDMENT OF REGISTRATION RIGHTS

     This Agreement may be amended and the obligations hereunder may be waived
(either generally or in a particular instance, and either retroactively or
prospectively) only with the written consent of the Company and of the Investors
who then hold a majority in interest of the Registrable Securities (but not
including any Investor who is not affected by such amendment or

                                       12
<PAGE>

waiver). Any amendment or waiver effected in accordance with this Article X is
binding upon each Investor and the Company. Notwithstanding the foregoing, no
amendment or waiver will retroactively affect any Investor without its consent,
or will prospectively adversely affect any Investor who no longer owns any
Registrable Securities without its consent. Neither Article VI nor Article VII
hereof may be amended or waived in a manner adverse to an Investor without its
consent.

                                  ARTICLER XI
                                 MISCELLANEOUS

     11.1 Conflicting Instructions. A person or entity is deemed to be a holder
          ------------------------
of Registrable Securities whenever such person or entity owns of record such
Registrable Securities. If the Company receives conflicting instructions,
notices or elections from two or more persons or entities with respect to the
same Registrable Securities, the Company will act upon the basis of
instructions, notice or election received from the registered owner of such
Registrable Securities.

     11.2 Notices. Any notices required or permitted to be given under the terms
          -------
of this Agreement will be given as set forth in the Purchase Agreement.


     11.3 Waiver. Failure of any party to exercise any right or remedy under
          ------
this Agreement or otherwise, or delay by a party in exercising such right or
remedy, does not operate as a waiver thereof.

     11.4 Governing Law.  This Agreement will be governed by and interpreted in
          -------------
accordance with the laws of the State of California without regard to the
principles of conflict of laws.  The parties hereto hereby submit to the
exclusive jurisdiction of the United States federal and state courts located in
the State of California with respect to any dispute arising under this
Agreement, the agreements entered into in connection herewith or the
transactions contemplated hereby or thereby.

     11.5 Severability. If any provision of this Agreement is invalid or
          ------------
unenforceable under any applicable statute or rule of law, then such provision
will be deemed modified in order to conform with such statute or rule of law.
Any provision hereof that may prove invalid or unenforceable under any law will
not affect the validity or enforceability of any other provision hereof.

     11.6 Entire Agreement. This Agreement and the Purchase Agreement,
          ----------------
(including all schedules and exhibits thereto) constitute the entire agreement
among the parties hereto with respect to the subject matter hereof and thereof.
There are no restrictions, promises, warranties or undertakings, other than
those set forth or referred to herein or therein. This Agreement supersedes all
prior agreements and understandings among the parties hereto with respect to the
subject matter hereof.

     11.7 Successors and Assigns. Subject to the requirements of Article 9
          ----------------------
hereof, this Agreement inures to the benefit of and is binding upon the
successors and assigns of each of the parties hereto.

                                       13
<PAGE>

     11.8 Use of Pronouns. All pronouns refer to the masculine, feminine or
          ---------------
neuter, singular or plural, as the context may require.


     11.9 Headings. The headings of this Agreement are for convenience of
          --------
reference only, are not part of this Agreement and do not affect its
interpretation.


     11.10 Counterparts. This Agreement may be executed in two or more
           ------------
counterparts, each of which is deemed an original but all of which constitute
one and the same agreement. This Agreement, once executed by a party, may be
delivered to the other party hereto by facsimile transmission, and facsimile
signatures are binding on the parties hereto. In the event any signature is
delivered by facsimile transmission, the party using such means of delivery
shall cause the manually executed pages to be physically delivered to the other
party within 5 business days of the execution hereof.

    11.11 Further Assurances. Each party will do and perform, or cause to be
          ------------------
done and performed, all such further acts and things, and will execute and
deliver all other agreements, certificates, instruments and documents, as
another party may reasonably request in order to carry out the intent and
accomplish the purposes of this Agreement and the consummation of the
transactions contemplated hereby.

     11.12 Consents. All consents and other determinations to be made by the
           --------
Investors pursuant to this Agreement will be made by the Initial Investors or
the Investors holding a majority in interest of the Registrable Securities.

     11.13 No Strict Construction. The language used in this Agreement is deemed
           ----------------------
to be the language chosen by the parties to express their mutual intent, and no
rules of strict construction will be applied against any party.

                                       14
<PAGE>

     IN WITNESS WHEREOF, the undersigned Investors and the Company have caused
this Agreement to be duly executed as of the date first above written.

                              COMPANY:

                              GREATER BAY BANCORP.



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


                      [Signatures continued on next page]

                                       15
<PAGE>

                              INVESTOR: FRANKLIN SMALL CAP GROWTH FUND


                              By: /s/ Murray L. Simpson
                                  ------------------------------
                                  Name: Murray L. Simpson
                                  Its:  Vice President

                              INVESTOR: EMERGING SMALL COMPANY TRUST


                              By: /s/ Murray L. Simpson
                                  ------------------------------
                                  Name: Murray L. Simpson
                                  Its:  Vice President

                              INVESTOR: U.S. SMALL CAP FUND


                              By: /s/ Murray L. Simpson
                                  ------------------------------
                                  Name: Murray L. Simpson
                                  Its:  Vice President

                              INVESTOR: FRANKLIN SMALL CAP INVESTMENTS FUND


                              By: /s/ Murray L. Simpson
                                  ------------------------------
                                  Name: Murray L. Simpson
                                  Its:  Vice President

                              INVESTOR: MERRILL LYNCH GLOBAL FINANCIAL
                                        SERVICES PORTFOLIO, INC.

                              By: /s/ James Ellman
                                  ------------------------------
                                  Name: James Ellman
                                  Its:  Vice President and Portfolio Manager

                              INVESTOR: MERRILL LYNCH EQUITY CONVERTIBLE SERIES-
                                        FINANCIAL SERVICES PORTFOLIO

                              By: /s/ Andrea Mitroff
                                  ------------------------------
                                  Name: Andrea Mitroff
                                  Its:  Assistant Portfolio Manager

                                       16
<PAGE>

                              INVESTOR: LAWRENCE OFFSHORE PARTNERS, LLC


                              By: /s/ Lawrence Garshofsky
                                  ------------------------------
                                  Name: Lawrence Garshofsky
                                  Its:  Manager

                              INVESTOR: LAWRENCE PARTNERS, LP


                              By: /s/ Lawrence Garshofsky
                                  ------------------------------
                                  Name: Lawrence Garshofsky
                                  Its:  Manager

                              INVESTOR: SUNOVA LONG-TERM OPPORTUNITY FUND, LP


                              By: /s/ Matthew Byrnes
                                  -------------------------------
                                  Name: Matthew Byrnes
                                  Its:  Managing Partner

                              INVESTOR: MALTA OFFSHORE, LTD
                                        SANDLER O'NEILL ASSET MANAGEMENT

                              By:  /s/ Terry Maltese
                                   ------------------------------
                                  Name: Terry Maltese
                                  Its:  President

                              INVESTOR: MALTA HEDGE FUND II, LP
                                        SANDLER O'NEILL ASSET MANAGEMENT

                              By:  /s/ Terry Maltese
                                   -------------------------------
                                  Name: Terry Maltese
                                  Its:  President

                              INVESTOR: MALTA HEDGE FUND, LP
                                        SANDLER O'NEILL ASSET MGMT

                              By:  /s/ Terry Maltese
                                   -------------------------------
                                  Name: Terry Maltese
                                  Its:  President

                                       17
<PAGE>

                              INVESTOR: MALTA PARTNERS II,LP
                                        SANDLER O'NEILL ASSET MGMT


                              By: /s/ Terry Maltese
                                  --------------------------------
                                  Name: Terry Maltese
                                  Its:  President

                              INVESTOR: MALTA PARTNERS, LP
                                        SANDLER O'NEILL ASSET MGMT


                              By: /s/ Terry Maltese
                                  --------------------------------
                                  Name: Terry Maltese
                                  Its:  President

                              INVESTOR: NORTHAVEN PARTNERS, L.P.


                              By: /s/ Paul Burke
                                  --------------------------------
                                  Name: Paul Burke
                                  Its:  Member of General Partner

                              INVESTOR: NORTHAVEN PARTNERS II, L.P.


                              By: /s/ Paul Burke
                                  --------------------------------
                                  Name: Paul Burke
                                  Its:  Member of GP

                              INVESTOR: NORTHAVEN PARTNERS III,L.P.


                              By: /s/ Paul Burke
                                  --------------------------------
                                  Name: Paul Burke
                                  Its:  Member of GP

                              INVESTOR: BANC FUND V, L.P.


                              By: /s/ Charles J. Moore
                                  ---------------------------------
                                  Name: Charles J. Moore
                                  Its:  Member

                                       18
<PAGE>

                              INVESTOR: BANK FUND III TRUST


                              By: /s/ Charles J. Moore
                                  ---------------------------------
                                  Name: Charles J. Moore
                                  Its:  Member

                              INVESTOR: BANC FUND III, L.P.


                              By: /s/ Charles J. Moore
                                  --------------------------------
                                  Name: Charles J. Moore
                                  Its:  Member

                              INVESTOR: MUTUAL FINANCIAL SERVICES FUND


                              By: /s/ Raymond Garea
                                  ---------------------------------
                                  Name: Raymond Garea
                                  Its:  Senior Vice President

                              INVESTOR: NICHOLAS-APPLEGATE PACIFIC
                                        CENTURY TRUST #2 SMALL

                              By: /s/ Scott A. Long
                                  ---------------------------------
                                  Name: Scott A. Long
                                  Its:  Head of Global Operations

                              INVESTOR: NICHOLAS-APPLEGATE SMALL CAP VALUE

                              By: /s/ Scott A. Long
                                  ---------------------------------
                                  Name: Scott A. Long
                                  Its:  Head of Global Operations

                              INVESTOR: NICHOLAS-APPLEGATE CORNERSTONE/SHEPERD
                                        VALUE

                              By: /s/ Scott A. Long
                                  ---------------------------------
                                  Name: Scott A. Long
                                  Its:  Head of Global Operations

                                      19