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In 2000, Hwang and Li proposed a new remote user authentication scheme using smart cards. Chan-Cheng, 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 et al showed that the modified scheme is still vulnerable to some previous attacks. In 2004, Kumar proposed a new scheme to solve these problems. In this paper, we find out that some weaknesses still exist in Kumar's scheme and present a modified remote user authentication and key agreement scheme using smart cards to conquer them. The proposed scheme also generates a common session key.