Exhibit
      10.4


    AMENDMENT
      AGREEMENT

     

    AMENDMENT
      AGREEMENT (this “Agreement”),
      dated
      as of May 22, 2007, among Gigabeam Corporation (the “Company”),
      Midsummer Investment, Ltd. (“Midsummer”),
      Feldman Weinstein & Smith LLP (the “Agent”),
      Louis
      Slaughter and Douglas Lockie (Messrs. Slaughter and Lockie, the “Pledgors”).

     

    Preliminary
      Statement:

     

    WHEREAS,
      Midsummer was issued a 14% Secured Promissory Note (the “Note”)
      of the
      Company which was secured by a pledge of certain shares of common stock of
      the
      Company owned by the Pledgors (the “Pledged
      Shares”)
      pursuant to that certain Pledge and Security Agreement, dated April 17, 2007
      by
      and among the parties hereto (the “Pledge
      Agreement”)
      Capitalized terms used and not otherwise defined herein that are defined in
      the
      Pledge Agreement.

     

    WHEREAS,
      pursuant to the Securities Purchase Agreement of even date herewith entered
      into
      by and among the Company and the purchasers signatory thereto, including
      Midsummer, Midsummer shall purchase 14% Secured Debentures (the “Debentures”)
      partially through the surrender of all of the principal of, and accrued but
      unpaid interest on, the Notes on a $1 for $1 basis.

     

    WHEREAS,
      pursuant to the terms of the Pledge Agreement, upon payment in full of the
      Notes, the Pledged Shares would be returned to the Pledgors and the pledge
      terminated. 

     

    WHEREAS,
      subject to the terms and conditions set forth herein, the Pledgors agree to
      amend the terms of the Pledge Agreement such that, upon surrender of the Notes
      to the Company and issuance of the Debentures, the obligations of the Company
      under the Debentures are secured by a pledge of the Pledged Shares.

     

    NOW,
      THEREFORE, the parties to this Agreement, for adequate and sufficient
      consideration, the receipt of which is hereby acknowledged do hereby agree
      as
      follows:

     

    1.  Amendment
      to definition of “Obligations”.
      The
      definition of “Obligations” under the Pledge Agreement is hereby amended to
      include all present and future indebtedness, obligations, covenants, duties
      and
      liability of any kind or nature of the Company to the Pledgees now existing
      or
      hereafter arising under or in connection with this Agreement, the Debentures
      and
      the other agreement entered into in connection therewith.

     

    2.  Amendment
      to Termination Provision of the Pledge Agreement.
      The
      second sentence of Section 15 of the Pledge Agreement is hereby amended and
      restated as follows: Upon the earlier of (a) the indefeasible payment in full
      of
      the Obligations and (b) after the issuance of the Debentures, the date that
      the
      Company grants the holders of the Debentures a first priority security interest
      in all the assets of the Company, the security interest granted hereby shall
      terminate and all rights to the Pledged Collateral shall revert to the
      Pledgors.”

     

    3.  Effect
      on Pledge Agreement. Except
      as
      expressly set forth above, all of the terms and conditions of the Pledge
      Agreement shall continue in full force and effect after the execution of this
      Agreement and shall not be in any way changed, modified or superseded by the
      terms set forth herein.

     

    
      
        
        

      

      
        
        

        
          

        

      

      
        
        

      

    

     

    4.  Amendments
      and Waivers.
      The
      provisions of this Agreement, including the provisions of this sentence, may
      not
      be amended, modified or supplemented, and waivers or consents to departures
      from
      the provisions hereof may not be given, unless the same shall be in writing
      and
      signed by the Company, each Pledgor, the Agent and Midsummer. 

     

    5.  Notices.
      Any and
      all notices or other communications or deliveries required or permitted to
      be
      provided hereunder shall be delivered as set forth in the Pledge Agreement.
      

     

    6.  Successors
      and Assigns.
      This
      Agreement shall inure to the benefit of and be binding upon the successors
      and
      permitted assigns of each of the parties. The Pledgors may not assign their
      rights or obligations hereunder without the prior written consent of Midsummer.
      Each Holder may assign their respective rights hereunder in the manner and
      to
      the Persons as permitted under the applicable Purchase Agreement.

     

    7.  Execution
      and Counterparts.
      This
      Agreement may be executed in two or more counterparts, all of which when taken
      together shall be considered one and the same agreement and shall become
      effective when counterparts have been signed by each party and delivered to
      the
      other party, it being understood that both parties need not sign the same
      counterpart. In the event that any signature is delivered by facsimile
      transmission or by e-mail delivery of a “.pdf” format data file, such signature
      shall create a valid and binding obligation of the party executing (or on whose
      behalf such signature is executed) with the same force and effect as if such
      facsimile or “.pdf” signature page were an original thereof.

     

    8.  Governing
      Law.
      All
      questions concerning the construction, validity, enforcement and interpretation
      of this Agreement shall be determined in accordance with the provisions of
      the
      Pledge Agreement.

     

    9.  Severability.
      If any
      term, provision, covenant or restriction of this Agreement is held by a court
      of
      competent jurisdiction to be invalid, illegal, void or unenforceable, the
      remainder of the terms, provisions, covenants and restrictions set forth herein
      shall remain in full force and effect and shall in no way be affected, impaired
      or invalidated, and the parties hereto shall use their commercially reasonable
      efforts to find and employ an alternative means to achieve the same or
      substantially the same result as that contemplated by such term, provision,
      covenant or restriction. It is hereby stipulated and declared to be the
      intention of the parties that they would have executed the remaining terms,
      provisions, covenants and restrictions without including any of such that may
      be
      hereafter declared invalid, illegal, void or unenforceable.

     

    10.  Headings.
      The
      headings in this Agreement are for convenience only, do not constitute a part
      of
      the Agreement and shall not be deemed to limit or affect any of the provisions
      hereof.

     

    [SIGNATURE
      PAGE FOLLOWS]

     

    
      
        
        

      

      
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    IN
      WITNESS WHEREOF, the parties hereto have caused this Amendment Agreement to
      be
      duly executed by their respective authorized signatories as of the date first
      indicated above.       

    
      	 	 	 
	 	 	PLEDGORS: 
	 
 	 
 	 
 
	
            	
            	/s/Louis S. Slaughter
	 	
              
Louis
              Slaughter


    

     

    
      	 	 	
            
	
            	
            	/s/Douglas G. Lockie
	 	
              
Douglas
              Lockie


    

     

     

    
      	 	 	
              THE COMPANY:

               

              GIGABEAM CORPORATION

            
	 
 	 
 	 
 
	
            	
            	By: /s/
              Louis S. Slaughter
	 	
              
                
Name:

            
	 	
              Title:

            


    

     

    
      	
              AGENT:

               

              FELDMAN
                WEINSTEIN & SMITH LLP

            	 	 	 
	 	 	 	 
	 	 	 	 
	By: /s/Robert
              F. Charron	 	 	
            
	
              
                
Name:
                Robert F. Charron

            	 	 	
            
	
              Title:
                Authorized Signatory

            	 	 	
            


    

     

    


    
      	
              MIDSUMMER
                INVESTMENT, LTD.

            	 	 	 
	 	 	 	 
	 	 	 	 
	By: /s/Scott
              D. Kaufman	 	 	
            
	
              
                
Name:
                Scott D. Kaufman

            	 	 	
            
	
              Title:
                Managing Director of Midsummer Capital, LLC as investment advisor
                to
                Midsummer Investment,
                Ltd.

            	 	 	
            


    

     

    [REMAINDER
      OF PAGE INTENTIONALLY LEFT BLANK

    SIGNATURE
      PAGE FOR PLEDGEES FOLLOWS]

    


    
      
        
        

      

      
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