THETERMS AND CONDITIONS OF THE WARRANTS OFFERING ARE SET FORTH IN THE COMPANYS PROSPECTUS SUPPLEMENT DATED SEPTEMBER 4, 2015 (THE PROSPECTUS) AND ARE INCORPORATED HEREIN BY REFERENCE. COPIES OFTHE PROSPECTUS ARE AVAILABLE UPON REQUEST FROM BROADRIDGE CORPORATE ISSUER SOLUTIONS, INC., THE WARRANTS AGENT. Stereotaxis, Inc. Incorporated under the laws of the State of Delaware TRANSFERABLE SUBSCRIPTION WARRANTS CERTIFICATE Evidencing Transferable Subscription Warrants to Purchase Shares of Common Stock of Stereotaxis, Inc. SubscriptionPrice: $1.10 per Share THE SUBSCRIPTION WARRANTS WILL EXPIRE IF NOT EXERCISED ON OR BEFORE 5:00 P.M., EASTERN TIME, ON SEPTEMBER 30, 2015 UNLESS EXTENDED BY STEREOTAXIS, INC.

Exhibit 4.1

NUMBER OF WARRANTS:                     

THE TERMS AND CONDITIONS OF THE WARRANTS OFFERING ARE SET FORTH IN

THE COMPANY’S PROSPECTUS SUPPLEMENT

DATED SEPTEMBER 4, 2015 (THE “PROSPECTUS”) AND ARE INCORPORATED

HEREIN BY REFERENCE.

COPIES OF THE PROSPECTUS ARE AVAILABLE UPON REQUEST FROM

BROADRIDGE CORPORATE ISSUER SOLUTIONS, INC., THE WARRANTS AGENT.

Stereotaxis, Inc.

Incorporated under the laws of the State of Delaware

TRANSFERABLE SUBSCRIPTION WARRANTS CERTIFICATE

Evidencing Transferable Subscription Warrants to Purchase Shares of Common Stock

of Stereotaxis, Inc.

Subscription Price: $1.10 per Share

THE SUBSCRIPTION WARRANTS WILL EXPIRE IF NOT EXERCISED ON OR

BEFORE 5:00 P.M., EASTERN TIME,

ON SEPTEMBER 30, 2015 UNLESS EXTENDED BY STEREOTAXIS, INC.

REGISTERED OWNER:

THIS CERTIFIES THAT the registered owner whose name is inscribed hereon is the owner of the number of transferable subscription warrants (“Warrants”) set forth above. Each whole Warrant entitles the holder thereof to subscribe for and purchase one share of Common Stock, par value $0.001 per share, of Stereotaxis, Inc., a Delaware corporation, at a subscription price of $1.10 per share (the “Subscription Privilege”), pursuant to a warrants offering (the “Warrants Offering”), on the terms and subject to the conditions set forth in the Prospectus and the “Instructions as to Use of Stereotaxis, Inc. Warrants Certificates” accompanying this Subscription Warrants Certificate. If any shares of Common Stock available for purchase in the Warrants Offering are not purchased by other holders of Warrants pursuant to the exercise of the Subscription Privilege (the “Excess Shares”), any Warrants holder that exercises its Subscription Privilege in full may subscribe for a number of Excess Shares pursuant to the terms and conditions of the Warrants Offering, subject to proration and certain limitations and allocations, as described in the Prospectus (the “Over-Subscription Privilege”). The Warrants represented by this Subscription Warrants Certificate may be exercised by completing Form 1 and any other appropriate forms on the reverse side hereof and by returning the full payment of the subscription price for each share of Common Stock in accordance with the “Instructions as to Use of Stereotaxis, Inc. Warrants Certificates” that accompany this Subscription Warrants Certificate.

This Subscription Warrants Certificate is not valid unless countersigned by the subscription agent and registered by the registrar. Witness the seal of Stereotaxis, Inc. and the signatures of its duly authorized officers.

Dated:

DELIVERY OPTIONS FOR SUBSCRIPTION WARRANTS CERTIFICATE

Delivery other than in the manner or to the addresses listed below will not constitute valid delivery.

By hand or overnight courier:

Broadridge Corporate Issuer Solutions, Inc.

Attn: BCIS IWS

51 Mercedes Way

Edgewood, NY 11717

By mail:*

Broadridge Corporate Issuer Solutions, Inc.

Attn: Re-Organization Dept., P.O. Box 1317

Brentwood, NY 11717.

PLEASE PRINT ALL INFORMATION CLEARLY AND LEGIBLY.

FORM 1-EXERCISE OF SUBSCRIPTION PRIVILEGE

To subscribe for shares pursuant to your Subscription Privilege, please complete lines (a) and (c) and sign under Form 4 below. To subscribe for shares pursuant to your Over-Subscription Privilege, please also complete line (b) and sign under Form 4 below. To the extent you subscribe for more Shares than you are entitled under either the Subscription Privilege or the Over-Subscription Privilege, you will be deemed to have elected to purchase the maximum number of Shares for which you are entitled to subscribe under the Subscription Privilege or Over-Subscription Privilege, as applicable.

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METHOD OF PAYMENT (CHECK ONE)

Bank Name: U.S. Bank

ABA/Routing Number: 123000848

International/Swift Code: USBKUS44IMT

Address: 800 Nicollet Mall

            Minneapolis, MN 55402 USA

Beneficiary Account Name: Broadridge

Account Number: 153910728465

FCC: Broadridge FBO Stereotaxis, Inc.

FFC: a/c 153910726998

FORM 2-TRANSFER TO DESIGNATED TRANSFEREE

To transfer your Warrants to another person, complete this Form 2 and have your signature guaranteed under Form 6.

For value received,                      of the Warrants represented by this Subscription Warrants Certificate are assigned to:

IMPORTANT: The signature(s) must correspond with the name(s) as printed on the reverse of this Subscription Warrants Certificate in every particular, without alteration or enlargement, or any other change whatsoever.

FORM 3-DELIVERY TO DIFFERENT ADDRESS

If you wish for the Common Stock underlying your Warrants, a certificate representing unexercised Warrants or the proceeds of any sale of Warrants to be delivered to an address different from that shown on the face of this Subscription Warrants Certificate, please enter the alternate address below, sign under Form 4 and have your signature guaranteed under Form 6.

FORM 4-SUBSCRIPTION AUTHORIZATION: I acknowledge that I have received the Prospectus for the Warrants Offering and I hereby irrevocably subscribe for the number of shares of Common Stock indicated above on the terms and conditions set forth in the Prospectus.

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FORM 5-ACKNOWLEDGEMENT:

I acknowledge receipt of the Prospectus and understand that, after delivery to Broadridge Corporate Issuer Solutions, Inc., as Warrants Agent, I may not modify or revoke the subscription for shares indicated in this Subscription Warrants Certificate. Under penalties of perjury, I certify that the information contained herein, including the social security number or taxpayer identification number given above, is correct.

The signature below must correspond with the name of the registered holder exactly as it appears on the books of the Company’s transfer agent without any alteration or change whatsoever.

If signature is by a trustee(s), executor(s), administrator(s), attorney(s)-in-fact, officer(s) of a corporation or another acting in a fiduciary or representative capacity, please provide the following information (please print).

FORM 6-GUARANTEE OF SIGNATURES: All Warrants holders who specify special or delivery instructions must have their signatures guaranteed by an Eligible Guarantor Institution, as defined in Rule 17Ad-15 of the Securities and Exchange Act of 1934, as amended.

IMPORTANT: The signature(s) should be guaranteed by an eligible guarantor institution (bank, stock broker, savings & loan association or credit union) with membership in an approved signature guarantee medallion program pursuant to Securities and Exchange Commission Rule 17Ad-15.

FOR INSTRUCTIONS ON THE USE OF STEREOTAXIS, INC. SUBSCRIPTION WARRANTS

CERTIFICATES, CONSULT BROADRIDGE CORPORATE ISSUER SOLUTIONS, INC., THE WARRANT

AGENT, AT ###-###-####.

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