Exhibit 99.2

Press Release dated March 17, 2004

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

FOR IMMEDIATE RELEASE

GREATER BAY BANCORP ANNOUNCES PROPOSED OFFERING

OF ZERO COUPON SENIOR CONVERTIBLE DEBT SECURITIES

PALO ALTO, Calif., March 17, 2004—Greater Bay Bancorp (Nasdaq:GBBK), a $7.6 billion in assets financial services holding company, today announced that it intends to raise up to $200 million through a private offering of zero coupon senior convertible debt securities due 2024. The Company also plans to grant to the initial purchaser of the debt securities an option to purchase up to an additional 20% in principal amount of the securities. The Company intends to use approximately $47 million of the net proceeds from the offering to repurchase its common stock concurrently with the offering and the remaining net proceeds for general corporate purposes.

The debt securities will be convertible into shares of the Company’s common stock upon the occurrence of specified events. The offering will be made only 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.