EXHIBIT 99.1 LA JOLLA PHARMACEUTICAL COMPANY ANNOUNCES EXERCISE OF OVER-ALLOTMENT OPTION SAN DIEGO, MARCH 5, 2004 - La Jolla Pharmaceutical Company announced today that the underwriter for its recently completed public offering of shares of common stock has purchased an additional 1,304,347 shares at the initial offering price per share pursuant to the over-allotment option granted to the underwriter in connection with the offering. The aggregate net proceeds to the Company from the offering, including the proceeds from the over-allotment shares, were approximately $29.5 million. Pacific Growth Equities, LLC served as the sole underwriter for the transaction. La Jolla Pharmaceutical Company is a biotechnology company developing therapeutics for antibody-mediated autoimmune diseases afflicting several million people in the United States and Europe. This press release contains forward-looking statements within the meaning of the Private Securities Litigation Reform Act of 1995. Such statements involve known and unknown risks, uncertainties and other factors that may cause actual results to differ materially from current expectations. ###