AMENDMENT TO WARRANTS OF STEREOTAXIS, INC.

Exhibit 4.7

AMENDMENT TO WARRANTS OF STEREOTAXIS, INC.

This Amendment to Warrants of Stereotaxis, Inc. (this “Amendment”) is made as of May 10, 2012, and amends warrants granted under (i) that certain Note And Warrant Purchase Agreement dated February 21, 2008, as amended by that certain First Amendment to Note and Warrant Purchase Agreement, made effective as of December 29, 2008, that certain Second Amendment to Note and Warrant Purchase Agreement, dated as of October 9, 2009, that certain Third Amendment to Note and Warrant Purchase Agreement, dated as of November 10, 2010, that certain Fourth Amendment to Note and Warrant Purchase Agreement, dated as of March 30, 2012, and that certain the Fifth Amendment to Note and Warrant Purchase Agreement, dated as of May 1, 2012 (as so amended, the “Note and Warrant Purchase Agreement”) by and among Stereotaxis, Inc., a Delaware corporation (the “Company”), Sanderling Venture Partners VI Co-Investment Fund, L.P., Sanderling VI Beteiligungs GmbH & Co KG, Sanderling VI Limited Partnership and Alafi Capital Company LLC and (ii) that certain Securities Purchase Agreement dated December 29, 2008 (the “Securities Purchase Agreement”) by and among Sanderling Venture Partners VI Co-Investment Fund, L.P., Sanderling VI Beteiligungs GmbH & Co KG, Sanderling VI Limited Partnership, Sanderling Ventures Management VI, and Alafi Capital Company LLC (collectively, the “Warrant Holders”) and the Company.

WHEREAS, a Warrant Holder currently holds each of Warrant Nos. 2008-1, 2008-2, 2008-3, 2008-4, 2009-1, 2009-2, 2009-3, 2009-4, 2009-5, 2009-6, 2009-7, 2009-8, 2010-1, 2010-2, 2010-3, 2010-4, 2012-1, 2012-2, 2012-3, 2012-4, 2012-5, 2012-6, 2012-7, and 2012-8 issued pursuant to the Note and Warrant Purchase Agreement (the “Credit Support Warrants”) and Warrant Nos. I1, I2, I3, I4, and I5 issued pursuant to the Securities Purchase Agreement (the “SPA Warrants,” and together with the Credit Support Warrants, the “Warrants”);

WHEREAS, the Warrant Holders, or their affiliates, and the Company are parties to the Note and Warrant Purchase Agreement, pursuant to which the Warrant Holders or their affiliates have extended a $10 million borrowing facility to the Company, the Committed Funds (as defined in the Note and Warrant Purchase Agreement) from each lender on a several (but not joint and several) basis;

WHEREAS, the Company and the Warrant Holders, or their affiliates, desire to enter into a Stock and Warrant Purchase Agreement, pursuant to which the Warrant Holders, or their affiliates, would purchase shares of the Company’s common stock and additional warrants to purchase the Company’s common stock;

WHEREAS, the Warrant Holders desire to waive the Company’s obligation to keep reserved, out of the authorized and unissued Common Stock, a number of shares sufficient for the exercise of the rights of purchase represented under the Warrants;

WHEREAS, the Warrant Holders constitute the Required Holders (as defined in the SPA Warrants);

NOW, THEREFORE, in consideration of the foregoing recitals and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, and intending to be legally bound, the Parties agree as follows:

1. Amendment of Share Reservation Requirements. Section 8 of Warrant Nos. 2008-1, 2008-2, 2008-3, 2008-4, 2009-1, 2009-2, 2009-3, 2009-4, 2009-5, 2009-6, 2009-7, 2009-8, 2010-1, 2010-2, 2010-3, 2010-4 and Section 1(g) of the SPA Warrants are hereby deleted in their entirety and replaced in each case with the following:

“Insufficient Authorized Shares. If at any time while this Warrant remains outstanding the Company does not have a sufficient number of authorized and unreserved shares of Common Stock to satisfy its obligation to reserve for issuance upon exercise of this Warrant at least a number of shares of Common Stock equal to (the “Required Reserve Amount”) the number of shares of Common Stock as shall from time to time be necessary to effect the exercise of all of this Warrant then outstanding (an “Authorized Share Failure”), then the Company shall, within 90 days after the occurrence of such Authorized Share Failure take action to increase the Company’s authorized and unissued shares of Common Stock to an amount sufficient to allow the Company to reserve the Required Reserve Amount for this Warrant then outstanding. The Company shall not be in breach of its obligation to reserve the Required Reserve Amount during such period so long as it is taking good faith efforts to satisfy its obligations under this covenant.”

2. Original Warrants in Full Force and Effect. Except as expressly modified by this Amendment, the terms of the Warrants shall continue in full force and effect without modification.

3. Titles and Subtitles; Construction. The titles of the Sections of this Amendment are for convenience of reference only and are not to be considered in construing this Amendment. All words used in this Amendment will be construed to be of such gender or number as the circumstances require.

4. Counterparts. This Amendment may be executed by facsimile and in any number of counterparts, each of which shall be deemed an original, and all of which together shall constitute one instrument.

5. Successors and Assigns. Except as otherwise expressly provided herein, the provisions hereof shall inure to the benefit of, and be binding upon, the successors, assigns, heirs, executors and administrators of the parties hereto.

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IN WITNESS WHEREOF, the Parties hereto have caused this Amendment to be signed by duly authorized officers or representatives, effective as of the date first written above.