117 1981, Lamport introduced a remote password authentication scheme using a password table. In 2000, Hwang and Li proposed a remote user authentication scheme using smart cards to solve the problems of Lamport scheme. First, Chan- Chang, Shen- Lin- Hwang and then Chang-Hwang pointed out some attacks on Hwang - Li's scheme. Shen-Lin- Hwang also proposed a modified scheme. In 2003, Leung-Cheng-Fong-Chan showed that a modified scheme proposed by Shen-Lin-Hwang is still vulnerable to all previous attacks. This paper presents a new remote user authentication scheme. This scheme is secure against Chan Cheng and all the extendcd attacks (1).