Exhibit 99.1

FOR IMMEDIATE RELEASE

Contacts:

Stereotaxis, Inc.
314-615-6957
Jim Stolze
jstolze@stereotaxis.com Euro RSCG Life NRP
212-845-4253
Ernie Knewitz (media)
ernie.knewitz@eurorscg.com

212-845-4269
Brian Ritchie (investors)
brian.ritchie@eurorscg.com

STEREOTAXIS ANNOUNCES UNDERWRITERS’ EXERCISE
OF OPTIONAL SHARES

ST. LOUIS, MO, September 3, 2004 — Stereotaxis, Inc. (Nasdaq: STXS) announced today that the underwriters for the recently completed initial public offering of Stereotaxis have exercised their option to purchase an additional 462,352 shares of Stereotaxis common stock. All of the optional shares were sold by Stereotaxis. After giving effect to the sale of the optional shares, a total of 5,962,352 shares of common stock were publicly offered and sold by Stereotaxis at a price to the public of $8.00 per share. Goldman, Sachs & Co. acted as sole book-runner and co-lead manager with Bear, Stearns & Co. Inc. Deutsche Bank Securities and A.G. Edwards served as co-managers.

Copies of the final prospectus relating to Stereotaxis’ initial public offering may be obtained from Goldman, Sachs & Co.‘s Prospectus Department at 85 Broad Street, New York, New York, 10004, by telephone at 212-902-1171 or by faxing a request to 212-902-9316.

Stereotaxis designs, manufactures and markets an advanced cardiology instrument control system for use in a hospital’s interventional surgical suite to enhance the treatment of coronary artery disease and arrhythmias. The Stereotaxis System is designed to allow physicians to navigate catheters, guidewires and stent delivery devices through the blood vessels and chambers of the heart to treatment sites. This is achieved using computer-controlled, externally applied magnetic fields that govern the motion of the working tip of the catheter, guidewire or stent delivery device. All core components of the Stereotaxis System have received regulatory approval in the U.S. and Europe.

This press release shall not constitute an offer to sell or a solicitation of an offer to buy, nor will there be any sale of these securities in any state or jurisdiction in which such an offer, solicitation, or sale would be unlawful prior to registration or qualification under the securities laws of any such state or jurisdiction.

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