The fault cryptanalysis is a physical attack in which the key stored inside of the device can be extracted by occurring some faults when the device performs cryptographic algorithm. Since the international signature standard DSA(Digital Signature Algorithm) was known to be vulnerable to some fault analysis attacks, many researchers have been investigating the countermeasure to prevent these attacks. In this paper we propose a new countermeasure to compute DSA signature that has its immunity in the presence of faults. Since additional computational overhead of our proposal is only an inverse operation in signature process, the proposed DSA scheme can be implemented more efficiently compared to previous countermeasures.