STEREOTAXIS, INC. 2002 NON-EMPLOYEE DIRECTORS STOCK PLAN

Exhibit 10.4

STEREOTAXIS, INC.

2002 NON-EMPLOYEE DIRECTORS’ STOCK PLAN

(Amended and Restated May 29, 2008)

The purpose of the Stereotaxis, Inc. 2002 Non-Employee Directors Stock Plan (the “Plan”) is to strengthen the alignment of interests between non-employee Directors (“Participants”) and the shareholders of Stereotaxis, Inc. (the “Company”) through the increased ownership of shares of the Company’s common stock. This will be accomplished by allowing Participants to elect voluntarily to convert a portion or all of their fees for services as a Director into common stock and by granting Participants non-qualified options to purchase shares of common stock (“Stock Options”).

1. The Plan shall be administered by a committee (the “Committee”) appointed by of the Board of Directors of the Company (the “Board”), or, in the absence of any such Committee, the Board.

2. It shall be the duty of the Committee to administer the Plan in accordance with its provisions and to make such recommendations of amendments or otherwise as it deem necessary or appropriate. A decision by a majority of the Committee shall govern all actions of the Committee.

3. Subject to the express provisions of the Plan, the Committee shall have authority to allow Participants the right to elect to receive fees for services as a director in either cash or an equivalent amount of whole shares of Common Stock of the Company, or partly in cash and partly in whole shares of the Common Stock of the Company, subject to such conditions or restrictions, if any, as the Committee may determine. The Committee also has the authority to make all other determinations it deems necessary or advisable for administering the Plan.

4. The Committee may establish from time to time such regulations, provisions, and procedures within the terms of the Plan as, in its opinion, may be advisable in the administration of the Plan.

5. The Committee may designate the Secretary of the Company or other employees of the Company to assist the Committee in the administration of the Plan and may grant authority to such persons to execute documents on behalf of the Committee.

Participation in the Plan shall be limited to all non-employee Directors of the Company.

The total number of shares of Common Stock of the Company that may be awarded under Stock Options each year shall not be limited. The total number of shares of Common Stock of the Company that may be issued under the Plan shall initially be 300,000 shares, plus such aggregate number of shares otherwise available for grant under the Stereotaxis, Inc. 2002 Stock Incentive Plan at the time of any Stock Option award made hereunder.

Shares of common stock to be awarded under the terms of the Plan shall be treasury shares or authorized but unissued shares.

1. Each Participant shall, on the date of the Annual Meeting of stockholders during such Participant’s term,

automatically be granted a Stock Option to purchase a number of shares of Common Stock (which may include additional shares for the Chairman of the Board or other Participants as determined by the Board) (with such amount subject to adjustment as set forth in Article VII) as shall be determined by resolution of the Board from time to time, having an exercise price of one hundred percent (100%) of the fair market value (as determined in good faith by the Board) of the Common Stock on the date of grant. In addition, the Committee may grant other options to Participants from time to time.

2. The Stock Options shall have a term of ten (10) years from the date of grant, subject to earlier termination as provided herein, and shall be exercisable one (1) year from the date of grant (or such other date(s) as determined by the Committee), except in the case of death, in which case the Stock Options shall be immediately exercisable.

3. Stock Options are not transferable other than by will or by the laws of descent and distribution Legatees, distributees and duly appointed executors and administrators of the estate of a deceased Participant shall have the right to exercise such Stock Options at any time prior to the expiration date of the Stock Options.

4. If a Participant ceases to be a Director while holding unexercised Stock Options, such Director shall have up to one (1) year from the date of his or her termination of service in which to exercise any unexercised Stock Option(s), to the extent that the Director was entitled to exercise such Stock Option(s) at the date of his or her termination of service.

5. Upon the exercise of a Stock Option, payment in full of the exercise price shall be made by the Participant. The exercise price may be paid for by the Participant either in cash, shares of the Common Stock of the Company to be valued at their fair market value on the date of exercise, or a combination thereof.

6. For purposes of the Plan, a Change of Control means:

a. The purchase or other acquisition (other than from the Company) by any person, entity or group of persons, within the meaning of Section 13(d) or 14(d) of the Securities Exchange Act of 1934, as amended (the “Exchange Act”) (excluding, for this purpose, the Company or its subsidiaries or any employee benefit plan of the Company or its subsidiaries), of beneficial ownership (within the meaning of Rule 13d-3 promulgated under the Exchange Act) of 20% or more of either the then-outstanding shares of common stock of the Company or the combined voting power of the Company’s then-outstanding voting securities entitled to vote generally in the election of directors; or

b. Individuals who, as of the date hereof, constitute the Board of Directors of the Company (the “Board” and, as of the date hereof, the “Incumbent Board”) cease for any reason to constitute at least a majority of the Board, provided that any person who becomes a director subsequent to the date hereof whose election, or nomination for election by the Company’s shareholders, was approved by a vote of at least a majority of the directors then comprising the Incumbent Board (other than an individual whose initial assumption of office is in connection with an actual or threatened election contest relating to the election of directors of the Company, as such terms are used in Rule 14a-l 1 of Regulation 14A promulgated under the Exchange Act) shall be, for purposes of this section, considered as though such person were a member of the Incumbent Board; or

c. The consummation of a reorganization, merger or consolidation, in each case with respect to which persons who were the stockholders of the Company immediately prior to such reorganization, merger or consolidation do not, immediately thereafter, own more than 50% of, respectively, the common stock and the combined voting power entitled to vote generally in the election of directors of the reorganized, merged or consolidated corporation’s then-outstanding voting securities, or of a liquidation or dissolution of the Company or of the sale of all or substantially all of the assets of the Company.

The amount of shares authorized to be issued annually under the Plan will be subject to appropriate adjustment in the event of future stock splits, stock dividends, or other changes in capitalization of the Company to prevent the dilution or enlargement of rights under the Plan. The number and kind of shares and exercise prices covered by outstanding Stock Options and the number of shares to be granted as Stock Options pursuant to Article VI, paragraph 1 shall be adjusted to give effect to any such stock splits, stock dividends, combination or reclassification of shares, recapitalization, merger, or similar event.

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The Committee may transfer Common Stock of the Company under the Plan subject to such conditions or restrictions, if any, as the Committee may determine. The conditions and restrictions may vary from time to time and may be set forth in agreements between the Company and the Participant or in the awards of stock to them, all as the Committee determines.

1. The Board may, at any time, repeal the Plan or may amend it from time to time except that no such amendment may amend this paragraph, increase the annual aggregate number of shares subject to the Plan, or alter the persons eligible to participate in the Plan. The Participants and the Company shall be bound by any such amendments as of their effective dates, but if any outstanding awards are affected, notice thereof shall be given to the holders of such awards and such amendments shall not be applicable to such holder without his or her written consent. If the Plan is repealed in its entirety, all theretofore awarded shares subject to conditions or restrictions transferred pursuant to the Plan shall continue to be subject to such conditions or restrictions.

2. Every recipient of shares pursuant to the Plan shall be bound by the terms and provisions of the Plan and of the transfer of shares agreement referable thereto, and the acceptance of any transfer of shares pursuant to the Plan shall constitute a binding agreement between the recipient and the Company.

The Plan and each option hereunder shall be governed by the laws of the State of Delaware, excluding any conflicts or choice of law rule or principle that might otherwise refer construction or interpretation of the Plan to the substantive law of another jurisdiction. Recipients of options under the Plan are deemed to submit to the exclusive jurisdiction and venue of the federal or state courts of Missouri, County of St. Louis, to resolve any and all issues that may arise out of or relate to the Plan or any related option.

The Plan shall became effective as of March 25 2002.

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