EXHIBIT 99.1

Press Release dated March 23, 2004

For Information Contact
At Greater Bay Bancorp:	At Silverman Heller Associates:
Byron A. Scordelis, President and CEO	Philip Bourdillon/Gene Heller
(650) 614-5751	(310) 208-2550
Steven C. Smith, EVP and CFO
(650) 813-8222

FOR IMMEDIATE RELEASE

GREATER BAY BANCORP ANNOUNCES SALE

OF ZERO COUPON SENIOR CONVERTIBLE DEBT SECURITIES

PALO ALTO, Calif. – March 23, 2004 – Greater Bay Bancorp (Nasdaq:GBBK), a $7.6 billion in assets financial services holding company, today announced that it completed its private offering and sale of $265.2 million principal amount at maturity of its zero coupon senior convertible debt securities due 2024 with gross proceeds to the Company of $240.0 million. This amount includes $44.2 million principal amount at maturity of debt securities issued upon the exercise by the initial purchaser of its overallotment option.

The Company used approximately $47 million of the net proceeds from the sale to repurchase 1,695,273 shares of it common stock concurrently with the sale of the convertible debt securities. The Company intends to use the remaining net proceeds for general corporate purposes.

The debt securities were sold at an initial price of $904.95 per $1,000 principal amount at maturity representing a yield to maturity of 0.50%. Each $1,000 in principal amount at maturity is convertible into 23.7582 shares of the Company’s common stock (subject to adjustment in certain circumstances) upon the occurrence of certain events, including during any fiscal quarter if the sale price of the Company’s common stock is above 120% of the accreted conversion price measured over a specified number of trading days. This represents an initial conversion price of $38.09 per share of common stock, reflecting a premium of approximately 38% relative to the official Nasdaq closing price of the Company’s common stock of $27.60 on March 17, 2004. The Company may redeem all or some of the debt securities on or after March 23, 2009 at the issue price plus accreted issue discount to the redemption date. The Company may be required to repurchase the debt securities, at the option of the holders, on March 23, 2006, March 23, 2009, March 23, 2014 and March 23, 2019, at the issue price plus accreted issue discount to the repurchase date. The Company may also be required to repurchase the securities upon a change in control at the issue price plus accreted issue discount to the repurchase date.

The Company will pay contingent interest during any six month period commencing with the period beginning March 23, 2009, if the trading price of the securities exceeds 120% of the issue price plus accreted issue discount. The securities will mature on March 23, 2024.

The sale was made to qualified institutional buyers in reliance on Rule 144A under the Securities Act of 1933, as amended.

The senior convertible debt securities and the common stock issuable upon conversion of the securities have not been registered under the Securities Act and may not be offered or sold in the United States absent registration or an applicable exemption from registration under the Securities Act and applicable state securities laws. This press release does not constitute an offer to sell or the solicitation of an offer to buy, nor shall there be any sale of these securities in any state in which such offer, solicitation or sale would be unlawful.

Safe Harbor

This document may contain forward-looking statements that are subject to risks and uncertainties that could cause actual results to differ materially from those projected. For a discussion of factors that could cause actual results to differ, please see the publicly available Securities and Exchange Commission filings of Greater Bay Bancorp, including its Annual Report on Form 10-K for the year ended December 31, 2003 and particularly the discussion of risk factors within such documents.