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|CERTIFICATION PURSUANT TO                    
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|18 U.S.C. ss 1350, AS ADOPTED PURSUANT TO    
|SECTION 302 OF THE SARBANES-OXLEY ACT OF 2002

I, Jeffrey Finkelstein, certify that:

1. I have reviewed this annual report on Form 20-F of Argentex
Mining Corporation;

2. Based on my knowledge, this annual report does not contain
any untrue statement of a material fact or omit to state a material fact
necessary to make the statements made, in light of the circumstances under which
such statements were made, not misleading with respect to the period covered by
this annual report;

3. Based on my knowledge, the financial statements, and other
financial information included in this annual report, fairly present in all
material respects the financial condition, results of operations and cash flows
of the small business issuer as of, and for, the periods presented in this
annual report;

4 The small business issuers other certifying officer(s) and I
are responsible for establishing and maintaining disclosure controls and
procedures (as defined in Exchange Act Rules 13a-15(e) and 15d-15(e)) and
internal control over financial reporting (as defined in Exchange Act Rules
13a-15(f) and 15d-15(f)) for the small business issuer and have:

| | (a) | Designed such disclosure controls and procedures, or
      caused such disclosure controls and procedures to be designed under our
      supervision, to ensure that material information relating to the small
      business issuer, including its consolidated subsidiaries, is made known to
      us by others within those entities, particularly during the period in
      which this report is being prepared;                                        
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| | (b) | Designed such internal control over financial reporting,
      or caused such internal control over financial reporting to be designed
      under our supervision, to provide reasonable assurance regarding the
      reliability of financial reporting and the preparation of financial
      statements for external purposes in accordance with generally accepted
      accounting principles;                                                          
| |     |                                                                                                                                                                                                                                                                                                                                                                                                                                                                
| | (c) | Evaluated the effectiveness of the small business
      issuer's disclosure controls and procedures and presented in this report
      our conclusions about the effectiveness of the disclosure controls and
      procedures, as of the end of the period covered by this report based on
      such evaluation; and                                                                                                                                         
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| | (d) | Disclosed in this report any change in the small business
      issuer's internal control over financial reporting that occurred during
      the small business issuer's most recent fiscal quarter (the small business
      issuer's fourth fiscal quarter in the case of an annual report) that has
      materially affected, or is reasonably likely to materially affect, the
      small business issuer's internal control over financial
  reporting;

5. The small business issuers other certifying officer (s) and
I have disclosed, based on my most recent evaluation of internal control over
financial reporting, to the small business issuer's auditors and the audit
committee of the small business issuer's board of directors (or persons
performing the equivalent functions):

| | (a) | All significant deficiencies and material weaknesses in
      the design or operation of internal control over financial reporting which
      are reasonably likely to adversely affect the small business issuer's
      ability to record, process, summarize and report financial information;
      and
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| |     |                                                                                                                                                                                                                                                                                                             
| | (b) | Any fraud, whether or not material, that involves
      management or other employees who have a significant role in the small
      business issuer's internal control over financial
  reporting.                                                                                                         

|Date: April 26, 2013                                | 
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|                                                    | 
|/s/ Jeffrey
      Finkelstein                       | 
|Signature: Jeffrey Finkelstein                      | 
|Title: Chief Financial Officer (Principal           | 
|Financial Officer and Principal Accounting Officer) | 

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