Exhibit 99.1

CHESHIRE, Conn., Jan. 19 /PRNewswire-FirstCall/ — Alexion Pharmaceuticals, Inc. (Nasdaq: ALXN) today announced the pricing of $125 million aggregate principal amount of its Convertible Senior Notes due 2012 in a private placement to qualified institutional buyers, pursuant to Rule 144A under the Securities Act of 1933, as amended. The notes will bear interest at a rate of 1.375% per annum and be convertible into shares of Alexion’s common stock at an initial conversion rate of 31.7914 shares of common stock per $1,000 principal amount of notes, subject to adjustment (equivalent to a conversion price of approximately $31.46 per share and a conversion premium of approximately 35% to the last reported sale price of $23.30 per share on January 19, 2005). Alexion may not redeem any of the notes prior to maturity. Upon the occurrence of certain designated events prior to the maturity of the notes, subject to specified exceptions, investors will have the right to require Alexion to redeem the notes. Alexion has granted the initial purchasers of the notes an option to purchase up to an additional $25 million aggregate principal amount of the notes. The offering is expected to close on January 25, 2005.

Alexion expects to use the proceeds of the offering to retire its outstanding 5 ³/4 % Convertible Subordinated Notes due 2007 and for general corporate purposes.

The notes to be offered and the common stock issuable upon conversion of the notes have not been registered under the Securities Act of 1933, as amended, or any state securities laws, and may not be offered or sold in the United States absent registration or an applicable exemption from registration requirements.

This press release does not constitute an offer to sell, or the solicitation of an offer to buy, any security and shall not constitute an offer, solicitation or sale in any jurisdiction in which such offering would be unlawful.

This press release contains “forward-looking statements” within the meaning of the Private Securities Litigation Reform Act of 1995. These forward-looking statements include statements regarding Alexion’s intention to raise proceeds through the offering and sale of convertible notes, the intended use of proceeds and the anticipated terms of the notes. Among the important factors that could cause actual results to differ materially from those indicated by such forward-looking statements are Alexion’s ability to complete the offering on the anticipated terms or at all, general market conditions and other risks described in Alexion’s annual report on Form 10-K for the year ended July 31, 2004. Alexion is providing this information as of the date of this press release and does not undertake any obligation to update any forward-looking statement, whether as a result of new information, future events, or otherwise.

Alexion Pharmaceuticals, Inc.	Euro RSCG Life NRP
Leonard Bell, M.D.	Robert Stanislaro (Media)
Chief Executive Officer	(212) 845-4268
(203) 272-2596
Rhonda Chiger (Investors)
Rx Communications
(917) 322-2569

SOURCE Alexion Pharmaceuticals, Inc.