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In 1995, Wu proposed a remote login authentication scheme based on geometric approach without any password table. Wu’s scheme is humanization, simplicity, efficiency and beneficial to smart card. However, Chien, Jan and Tseng presented a cryptanalysis of Wu’s scheme to show that it is not secure. A modified version of Wu’s scheme was also proposed by them. In this paper, we shall point out that the modified remote login authentication scheme is still susceptible to password guessing attack. At the same time, we shall propose a solution to resist such attack.