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User authentication is an important technology to guarantee that only the legal users can access resources from the remote server. for user authentication, in 2011, Lee et al. proposed a dynamic user authentication scheme for multi-server environments. They claimed that this scheme provided efficiency, strong security, and user anonymity property. However, we find that Lee et al.'s scheme is still vulnerable to masquerade attack and cannot provide user anonymity. This paper will propose an improvement to remedy the weakness of Lee et al.'s scheme.