EXHIBIT 5.1

[GREATER BAY BANCORP LETTERHEAD]

August 6, 2004

Board of Directors

Greater Bay Bancorp

2860 West Bayshore Road

Palo Alto, CA 94303

Re: Registration Statement on Form S-3

Ladies and Gentlemen:

I am the general counsel of Greater Bay Bancorp, a California corporation (the “Company”) and, in such capacity, I have acted as counsel to the Company in connection with the preparation and filing under the Securities Act of 1933, as amended (the “Act”), of a Registration Statement on Form S-3 to be filed with the Securities and Exchange Commission on or about May 26, 2004 (the “Registration Statement”). The Registration Statement relates to the registration under the Act of $265,212,000 aggregate principal amount at maturity of its Zero Coupon Senior Convertible Contingent Debt Securities (“CODES”) due 2024 (the “Securities”) and the Company’s common stock, no par value per share (the “Shares”), issuable upon conversion and/or purchase of the Securities pursuant to that certain indenture, dated as of March 23, 2004, by and between the Company and Wilmington Trust Company, a Delaware banking corporation, as trustee (the “Indenture”). The Company issued the Securities pursuant to that certain purchase agreement, dated as of March 18, 2004 among the Company and Lehman Brothers Inc. (the “Purchase Agreement”). The Securities and the Shares are to be offered and sold by certain securityholders of the Company.

Other capitalized terms used but not defined herein have the meanings ascribed to them in the Registration Statement. As general counsel to the Company, I have been requested to render this opinion in accordance with the requirements of Item 601(b)(5) of Regulation S-K under the Act.

For the purpose of rendering the opinions set forth herein, I have been furnished with and examined only the following documents:

1. Restated Articles of Incorporation of the Company, as amended to date;

2. Bylaws of the Company, as amended to date;

3. Records of proceedings of the Board of Directors of the Company pertaining to the issuance of the Securities and the Shares;

4. The Registration Statement;

5. The Purchase Agreement;

6. The Indenture; and

7. The form of the Securities included in the form of Indenture, attached as Exhibit 4.1 to the Registration Statement.

With respect to all of the foregoing documents, I have assumed, without investigation, the genuineness of all signatures, the authenticity of all documents submitted to me as originals and the conformity to originals of all documents submitted to me as certified or reproduced copies. I also have obtained from the officers of the Company such advice as to such factual matters as I consider necessary for the purpose of this opinion, and insofar as this opinion is based on such matters of fact, I have relied on such advice.

Based upon the foregoing, I am of the opinion that:

1. The Securities are valid and binding obligations of the Company, enforceable against the Company in accordance with their terms, except to the extent enforcement thereof might be limited by (i) bankruptcy, insolvency, reorganization, moratorium, fraudulent conveyance, equitable subordination, or transfer laws or other similar laws affecting creditor’s rights generally, and (ii) general principles of equity.

2. The Shares initially issuable upon conversion of the Securities have been duly authorized and reserved for issuance and, when issued and delivered upon such conversion pursuant to the terms of the Indenture, will be validly issued, fully paid and non-assessable.

My opinion expressed herein is limited to those matters expressly set forth herein, and no opinion may be implied or inferred beyond the matters expressly stated herein. I hereby disclaim any obligation to notify any person or entity after the date hereof if any change in fact or law should change my opinion with respect to any matter set forth in this letter.

This opinion is limited to the current laws of the state of New York and the state of California, to present judicial interpretations thereof and to facts as they presently exist. In rendering this opinion, I have no obligation to supplement it should the current laws of the state of New York or the state of California be changed by legislative action, judicial decision or otherwise.

I hereby consent to the filing of this opinion as an exhibit to the Registration Statement and to the reference to me under the caption “Legal Matters” in the prospectus which is part of the Registration Statement.

Very truly yours,

/s/ Linda M. Iannone

Senior Vice President,

General Counsel and Secretary