CORTEX PHARMACEUTICALS, INC.

7,307,729 Shares of Common Stock

($0.001 par value)

This prospectus supplement supplements information contained in that certain prospectus dated December 8, 2003 of Cortex Pharmaceuticals, Inc. (the “Company”), relating to the offer and sale from time to time of up to 7,307,729 shares of the Company’s outstanding common stock issuable upon exercise of warrants, which are held by certain stockholders and warrant holders named in the prospectus under the section entitled “Selling Stockholders.” This prospectus supplement is not complete without, and may not be delivered or utilized except in connection with, the prospectus, including any amendments or supplements thereto.

The following amends the “Selling Stockholders” section set forth in the prospectus:

The table setting forth the names of the selling stockholders shall be amended to reflect the correct spelling of the name “Harlan Kleinman” to read “Harlan Kleiman.”

All information in this prospectus supplement is as of December 9, 2003.

The date of this prospectus supplement is December 9, 2003.