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Remote user authentication is a critical component of accessing remote services in distributed applications. In this paper we investigate the security vulnerabilities of a previously proposed remote user authentication scheme. After that we propose a security enhanced remote user password authentication scheme, which effectively prevents the adversary's attacks. The proposed authentication scheme is shown to be secure against password guessing attack, masquerade attack and replay attack. By performance analysis, the proposed scheme is shown to be very efficient, both in the computation and the storage cost. The proposed password authentication scheme is very suitable for providing remote authentication in distributed applications.