CERTIFICATED NOTE

Exhibit 4.5

CERTIFICATED NOTE

THIS NOTE IS NOT A SAVINGS ACCOUNT, DEPOSIT OR OTHER OBLIGATION OF ANY BANK OR NONBANK SUBSIDIARY OF GREATER BAY BANCORP AND IS NOT INSURED BY THE FEDERAL DEPOSIT INSURANCE CORPORATION OR ANY OTHER GOVERNMENT AGENCY.

THE HOLDER OF THIS NOTE BY ITS ACCEPTANCE HEREOF IS DEEMED TO HAVE AGREED TO BE BOUND BY THE PROVISIONS OF A REGISTRATION RIGHTS AGREEMENT BETWEEN GREATER BAY BANCORP AND THE INITIAL PURCHASER NAMED THEREIN, DATED APRIL 12, 2005 (THE “REGISTRATION RIGHTS AGREEMENT”). GREATER BAY BANCORP WILL PROVIDE A COPY OF THE REGISTRATION RIGHTS AGREEMENT TO A HOLDER WITHOUT CHARGE UPON WRITTEN REQUEST TO GREATER BAY BANCORP AT ITS PRINCIPAL PLACE OF BUSINESS.

THIS NOTE (OR ITS PREDECESSOR) HAS NOT BEEN REGISTERED UNDER THE UNITED STATES SECURITIES ACT OF 1933, AS AMENDED (THE “SECURITIES ACT”), AND, ACCORDINGLY, MAY NOT BE OFFERED, SOLD, PLEDGED OR OTHERWISE TRANSFERRED EXCEPT AS SET FORTH IN THE NEXT SENTENCE. BY ITS ACQUISITION HEREOF OR OF A BENEFICIAL INTEREST HEREIN, THE HOLDER:

(1) REPRESENTS THAT IT IS AN INSTITUTIONAL “ACCREDITED INVESTOR” (AS DEFINED IN RULE 50l(a)(1), (2), (3) OR (7) UNDER THE SECURITIES ACT) (AN “INSTITUTIONAL ACCREDITED INVESTOR”);

(2) REPRESENTS THAT IT IS PURCHASING THIS NOTE FOR INVESTMENT PURPOSES AND NOT WITH A VIEW TO, OR OFFFER OR SALE IN CONNECTION WITH, ANY DISTRIBUTION IN VIOLATION OF THE SECURITIES ACT;

(3) AGREES THAT IT WILL NOT RESELL OR OTHERWISE TRANSFER THIS NOTE PRIOR TO THE DATE WHICH IS THE LATER OF (X) TWO YEARS (OR SUCH SHORTER PERIOD OF TIME AS PERMITTED BY RULE 144(k) OF THE SECURITIES ACT) AFTER THE LATER OF THE ORIGINAL ISSUE DATE OF THE NOTES AND THE LAST DATE ON WHICH GREATER BAY BANCORP OR ANY “AFFILIATE” (AS DEFINED IN RULE 144 UNDER THE SECURITIES ACT) OF GREATER BAY BANCORP WAS THE OWNER OF THIS NOTE (OR ANY PREDECESSOR OF THIS NOTE) OR (Y) SUCH LATER DATE, IF ANY, AS MAY BE REQUIRED BY APPLICABLE LAW, EXCEPT (A) TO GREATER BAY BANCORP OR ANY OF ITS SUBSIDIARIES, (B) TO A PERSON WHOM THE SELLER REASONABLY BELIEVES IS A “QUALIFIED INSTITUTIONAL BUYER” (AS DEFINED IN RULE 144A UNDER THE SECURITIES ACT) (A “QIB”) PURCHASING FOR ITS OWN ACCOUNT OR FOR THE ACCOUNT OF A QIB IN A TRANSACTION MEETING THE REQUIREMENTS OF RULE 144A, (C) IN AN OFFSHORE TRANSACTION MEETING THE

REQUIREMENTS OF RULE 903 OR 904 OF REGULATION S UNDER THE SECURITIES ACT, (D) TO AN INSTITUTIONAL ACCREDITED INVESTOR THAT IS ACQUIRING A MINIMUM OF $100,000 AGGREGATE PRINCIPAL AMOUNT OF THIS NOTE OR SUCH INTEREST OR PARTICIPATION FOR ITS OWN ACCOUNT OR AS FIDUCIARY OR AGENT FOR OTHERS (EACH OF WHICH MUST BE SUCH AN INSTITUTIONAL ACCREDITED INVESTOR UNLESS THE PURCHASER IS A BANK (AS DEFINED IN SECTION 3(a)(2) OF THE SECURITIES ACT OR A SAVINGS AND LOAN ASSOCIATION OR OTHER INSTITUTION AS DESCRIBED IN SECTION 3(a)(5)(A) OF THE SECURITIES ACT, WHETHER ACTING IN ITS INDIVIDUAL CAPACITY OR IN A FIDUCIARY CAPACITY)) FOR INVESTMENT PURPOSES AND NOT WITH A VIEW TO, OR FOR OFFER OR SALE IN CONNECTION WITH, ANY DISTRIBUTION IN VIOLATION OF THE SECURITIES ACT (E) IN ACCORDANCE WITH ANOTHER EXEMPTION FROM THE REGISTRATION REQUIREMENTS OF THE SECURITIES ACT (AND BASED UPON AN OPINION OF COUNSEL ACCEPTABLE TO GREATER BAY BANCORP) OR (E) PURSUANT TO AN EFFECTIVE REGISTRATION STATEMENT UNDER THE SECURITIES ACT AND, IN EACH CASE, IN ACCORDANCE WITH THE APPLICABLE SECURITIES LAWS OF ANY STATE OF THE UNITED STATES OR ANY OTHER APPLICABLE JURISDICTION AND TO THE RIGHT OF GREATER BAY BANCORP TO REQUIRE THAT A LETTER IN THE FORM ATTACHED AS EXHIBIT K TO THE INDENTURE, DATED AS OF MARCH 24, 2003 BETWEEN GREATER BAY AND THE TRUSTEE, BE COMPLETED AND DELIVERED BY THE TRANSFEROR AND, IN CERTAIN CASES, THE TRANSFEREE TO THE TRUSTEE; AND

(4) AGREES THAT IT WILL DELIVER TO EACH PERSON TO WHOM THIS NOTE OR AN INTEREST HEREIN IS TRANSFERRED A NOTICE SUBSTANTIALLY TO THE EFFECT OF THIS LEGEND.

AS USED HEREIN, THE TERMS “OFFSHORE TRANSACTION” AND “UNITED STATES” HAVE THE MEANINGS GIVEN THEM BY RULE 902 OF REGULATION S UNDER THE SECURITIES ACT. THE INDENTURE GOVERNING THIS NOTE CONTAINS A PROVISION REQUIRING THE TRUSTEE TO REFUSE TO REGISTER ANY TRANSFER OF THIS NOTE IN VIOLATION OF THE FOREGOING.

GREATER BAY BANCORP

5.125% SENIOR NOTES, SERIES C, DUE 2010

GREATER BAY BANCORP, a California corporation (hereinafter called the “Company”, which term includes any successor corporation under the Indenture hereinafter referred to), for value received, hereby promises to pay to                     , or registered assigns, the

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principal sum of                      DOLLARS ($                    ) on April 15, 2010, and to pay interest thereon from April 15, 2005, or from the most recent Interest Payment Date (as defined below) to which interest has been paid or duly provided for, semiannually in arrears on April 15 and October 15 in each year, commencing October 15, 2005 (each an “Interest Payment Date”), at the rate of 5.125% per annum, until the principal hereof is paid or made available for payment. The interest so payable, and punctually paid or duly provided for, on any Interest Payment Date will, as provided in the Indenture, be paid to the Person in whose name this Note (or one or more Predecessor Notes) is registered at the close of business on the 15^th calendar day immediately preceding the relevant Interest Payment Date. Any such interest not so punctually paid or duly provided for will forthwith cease to be payable to the Holder on such Regular Record Date and may either be paid to the Person in whose name this Note (or one or more Predecessor Notes) is registered at the close of business on a Special Record Date for the payment of such Defaulted Interest to be fixed by the Trustee, notice whereof shall be given to Holders of Notes of this series not less than 10 days prior to such Special Record Date, or be paid at any time in any other lawful manner not inconsistent with the requirements of any securities exchange on which the Notes of this series may be listed, and upon such notice as may be required by such exchange, all as more fully provided in said Indenture. Interest for any full semiannual period will be computed on the basis of a 360-day year consisting of twelve 30-day months. The amount of interest payable for any partial semiannual period will be computed on the basis of the actual number of days elapsed during that period.

Payment of the principal of and any such interest on this Note will be made at the offices or agencies of the Company maintained for that purpose in Wilmington, Delaware, in such coin or currency of the United States of America as at the time of payment is legal tender for payment of public and private debts; provided, however, that at the option of the Company payment of interest may be made by check drawn upon any Paying Agent and mailed on or prior to an Interest Payment Date to the address of the Person entitled thereto as such address shall appear in the Security Register.

This Note is one of a duly authorized issue of securities of the Company (herein called the “Securities”), issued and to be issued under an Indenture, dated as of March 24, 2003, as amended and supplemented (the “Indenture”), between the Company and Wilmington Trust Company, a Delaware corporation (herein called the “Trustee”, which term includes any successor Trustee under the Indenture), to which Indenture and all Indentures supplemental thereto and Officers’ Certificates pursuant to Section 3.01 of the Indenture relating to the Notes, reference is hereby made for a statement of the respective rights of the Company, the Trustee and the Holders of the Securities, and the terms upon which the Securities are, and are to be, authenticated and delivered. This Note is one of a series of Securities of the Company designated as its 5.125% Senior Notes, Series C, due April 15, 2010 (herein called the “Notes”), initially limited in aggregate principal amount to $150,000,000. The Company may, without notice to, or the consent of, the Holders of the Notes, create and issue further Notes, equal in rank to the Notes in all respects (or in all respects except for the payment of interest accruing prior to the issue date of the new Securities or except for the first payment of interest following the issue date of the new Securities) so that the new Notes may be consolidated and form a single series with the Notes and have the same terms as the Notes.

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The Holder of this Note is entitled to the benefits of the Registration Rights Agreement, dated as of April 12, 2005, between the Company and the Initial Purchaser named therein (as the same may be amended from time to time, the “Registration Rights Agreement”). Capitalized terms used in this paragraph and not defined herein shall have the meanings assigned to them in the Registration Rights Agreement. In the event that (i) the Exchange Offer Registration Statement is not filed with the Securities Exchange Commission (the “Commission”) on or prior to the 120th day following April 15, 2005 (the “Closing Time”), (ii) the Exchange Offer Registration Statement is not declared effective by the Commission on or prior to the 180th day following the Closing Time, (iii) the Exchange Offer is not consummated on or prior to the 45th day following the effective date of the Exchange Offer Registration Statement, (iv) if required, a Shelf Registration Statement is not filed with the Commission on or prior to (A) the 180th day following the Closing Time or (B) the 75th day after the filing obligation arises, whichever is later, (v) if required, a Shelf Registration Statement is not declared effective on or prior to the 240th day following the Closing Time (or, if a Shelf Registration Statement is required to be filed upon the request of the Initial Purchaser, within 120 days after such request), (vi) a Shelf Registration Statement is declared effective by the Commission but such Shelf Registration Statement ceases to be effective or such Shelf Registration Statement or the Prospectus included therein ceases to be usable in connection with resales of Registrable Securities for any reason and (A) the aggregate number of days in any consecutive 365-day period for which the Shelf Registration Statement or such Prospectus shall not be effective or usable exceeds 90 days, (B) the Shelf Registration Statement or such Prospectus shall not be effective or usable for more than two periods (regardless of duration) in any consecutive 365-day period or (C) the Shelf Registration Statement or such Prospectus shall not be effective or usable for a period of more than 45 consecutive days, or (vii) the Exchange Offer Registration Statement is declared effective by the Commission but, if the Exchange Offer Registration Statement is being used in connection with the resale of Exchange Securities as contemplated by Section 3(f)(B) of the Registration Rights Agreement, the Exchange Offer Registration Statement ceases to be effective or the Exchange Offer Registration Statement or the Prospectus included therein ceases to be usable in connection with resales of Exchange Securities for any reason during the 90-day period referred to in Section 3(f)(B) of the Registration Rights Agreement (as such period may be extended pursuant to the last paragraph of Section 3 of the Registration Rights Agreement) and (A) the aggregate number of days in any consecutive 365-day period for which the Exchange Offer Registration Statement or such Prospectus shall not be effective or usable exceeds 90 days, (B) the Exchange Offer Registration Statement or such Prospectus shall not be effective or usable for more than two periods (regardless of duration) in any consecutive 365-day period or (C) the Exchange Offer Registration Statement or the Prospectus shall not be effective or usable for a period of more than 45 consecutive days (each of the events referred to in clauses (i) through (vii) above being hereinafter called a “Registration Default”), the per annum interest rate borne by the Registrable Securities shall be increased (“Additional Interest”) by one-quarter of one percent (0.25%) per annum immediately following such 120-day period in the case of clause (i) above, immediately following such 180-day period in the case of clause (ii) above, immediately following such 45-day period in the case of clause (iii) above, immediately following any such 180-day period or 75-day period, whichever ends later, in the case of clause (iv) above, immediately following any such 240-day period or 120-day period, whichever ends first, in the case of clause (v) above, immediately following the 90th day in any consecutive 365-day period, as of the first day of the third period in any consecutive 365-day period or immediately following the 45th consecutive day, whichever occurs first, that a Shelf Registration Statement shall not be effective or a Shelf Registration Statement or the Prospectus

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included therein shall not be usable as contemplated by clause (vi) above, or immediately following the 90th day in any consecutive 365-day period, as of the first day of the third period in any consecutive 365-day period or immediately following the 45th consecutive day, whichever occurs first, that the Exchange Offer Registration Statement shall not be effective or the Exchange Offer Registration Statement or the Prospectus included therein shall not be usable as contemplated by clause (vii) above; provided that the aggregate increase in such annual interest rate under this paragraph may in no event exceed one-quarter of one percent (0.25%) per annum; further provided that the aggregate increase in such annual interest rate may in no event be in excess of the rate permissible under applicable law. Upon the filing of the Exchange Offer Registration Statement after the 120-day period described in clause (i) above, the effectiveness of the Exchange Offer Registration Statement after the 180-day period described in clause (ii) above, the consummation of the Exchange Offer after the 45-day period described in clause (iii) above, the filing of the Shelf Registration Statement after the 180-day period or 75-day period, as the case may be, described in clause (iv) above, the effectiveness of a Shelf Registration Statement after the 240-day period or 120-day period, as the case may be, described in clause (v) above, the Shelf Registration Statement once again being effective or the Shelf Registration Statement and the Prospectus included therein becoming usable in connection with resales of Registrable Securities, as the case may be, in the case of clause (vi) above, or the Exchange Offer Registration Statement once again becoming effective or the Exchange Offer Registration Statement and the Prospectus included therein becoming usable in connection with resales of Exchange Securities, as the case may be, in the case of clause (vii) thereof, the interest rate borne by the Securities from the date of such filing, effectiveness, consummation or resumption of effectiveness or usability, as the case may be, shall be reduced to the original interest rate so long as no other Registration Default shall have occurred and shall be continuing at such time and the Company is otherwise in compliance with this paragraph; provided, however, that, if after any such reduction in interest rate, one or more Registration Defaults shall again occur, the interest rate shall again be increased pursuant to the foregoing provisions. The Company shall promptly provide the Trustee with notice of any change in the interest rate borne by this Note. Anything herein to the contrary notwithstanding, any Holder who was, at the time the Exchange Offer was pending and consummated, eligible to exchange, and did not validly tender, its Notes for Exchange Securities in the Exchange Offer will not be entitled to receive any Additional Interest.

This Note shall be subject to the Events of Default specified in paragraphs (1), (2), (5), (6), (7) and (8) of the Indenture.

This Note may not be redeemed prior to maturity.

As provided in the Indenture and subject to certain limitations set forth therein, the transfer of this Note may be registered in the Security Register of the Company upon surrender of this Note for registration of transfer at the office or agency of the Company in any place where the principal of and interest on this Note are payable, duly endorsed by, or accompanied by, a written instrument of transfer in form satisfactory to the Company, duly executed by the registered Holder hereof or his attorney duly authorized in writing, and thereupon one or more new Notes, of authorized denominations and for the same aggregate principal amount, will be issued to the designated transferee or transferees.

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This Note is issuable in minimum denominations of $100,000 and integral multiples of $1,000 in excess thereof. As provided in the Indenture, and subject to certain limitations set forth therein, this Note is exchangeable for a like aggregate principal amount of Notes of different authorized denominations, as requested by the Holder surrendering the same.

No service charge will be made for any such registration of transfer or exchange, but the Company may require payment of a sum sufficient to cover any tax or other governmental charge payable in connection therewith.

Prior to due presentment for registration of transfer of this Note, the Company, the Trustee and any agent of the Company or the Trustee may treat the Person in whose name this Note is registered as the owner hereof for the purpose of receiving payment as herein provided and for all other purposes, whether or not this Note be overdue, and neither the Company, the Trustee nor any such agent shall be affected by notice to the contrary.

If an Event of Default with respect to the Notes shall occur and be continuing, the principal and all unpaid interest hereof may be declared due and payable in the manner and with the effect provided in the Indenture and the Officers’ Certificate pursuant to Section 3.01 of the Indenture relating to the Notes.

The Indenture permits, with certain exceptions as therein provided, the amendment thereof and the modification of the rights and obligations of the Company and the rights of the Holders of the Securities of each series to be affected under the Indenture at any time by the Company and the trustee under each series to be affected with the consent of the Holders of a majority in principal amount of the Outstanding Securities of each series to be affected. The Indenture also contains provisions permitting the Holders of specified percentages in aggregate principal amount of the Outstanding Securities of any series, on behalf of the Holders of all Securities of such series, to waive compliance by the Company with certain provisions of the Indenture and certain past defaults under the Indenture and their consequences. Any such consent or waiver by the Holder of this Note shall be conclusive and binding upon such Holder and upon all future Holders of this Note and of any Notes issued upon the registration of transfer hereof or in exchange herefor or in lieu hereof whether or not notation of such consent or waiver is made upon this Note.

No reference herein to the Indenture and no provision of this Note or of the Indenture shall alter or impair the obligation of the Company, which is absolute and unconditional, to pay the principal of and interest, if any, on this Note at the times, place and rate, and in the coin and currency, herein prescribed.

This Note is governed by and construed in accordance with the internal laws of the State of New York without regard to its conflicts of law rules.

All terms used in this Note which are defined in the Indenture shall have the meanings assigned to them in the Indenture.

Unless the certificate of authentication hereon has been executed by the Trustee, directly or through an authenticating agent, by the manual signature of an authorized officer, this Note shall not be entitled to any benefit under the Indenture or be valid or obligatory for any purpose.

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IN WITNESS WHEREOF, the Company has caused this instrument to be duly executed.

Dated:                     , 2005

This is one of the Securities of the series designated herein referred to in the within-mentioned Indenture.

ASSIGNMENT

FOR VALUE RECEIVED the undersigned hereby sells, assigns and transfers unto

PLEASE INSERT SOCIAL SECURITY OR OTHER IDENTIFYING NUMBER OF ASSIGNEE

Name and address of assignee, including zip code, must be printed or typewritten)

the within Note, and all rights thereunder, hereby irrevocably constituting and appointing

Attorney to transfer said Note on the books of the within Company, with full power of substitution in the premises.

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