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Recently, Shen et al. proposed an improvement to Hwang-Li's scheme to prevent from forgery attack. However, Leung et al. pointed out that this improved scheme is still susceptible to forgery attack proposed by Chan and Cheng. Accordingly, the current paper presents an enhancement based on generalized ElGamal signature scheme to resolve such problems. As a result, the proposed scheme enables users to update their passwords freely without the help of a remote system, while also providing mutual authentication. In addition, the computational costs of this scheme are less than those of previously proposed schemes.