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Remote user authentication is important to protect web-based services offered over the Internet. The use of smart cards was proposed to avoid the storage of password table in the server. Further protection of user information in the smart cards can be done by imposing a fingerprint verification mechanism. The Lee, Ryu and Yoo (LRY) scheme which provides both smart card based authentication and fingerprint verification is found to be vulnerable to various attacks. This paper proposed an improvement to the LRY scheme which is able to withstand the attacks of the LRY scheme.