Sun proposed an efficient remote login authentication scheme based on one way hash function in 2000. In 2002, Chien et al. pointed out a deficiency of Sun’s scheme which only realized unilateral authentication and put forward an efficient and practical solution for remote mutual authentication scheme. But, recently Hsu discussed that this scheme was not secure enough since it was vulnerable to the parallel session attack again. In 2005, Liu et al. have proposed an enhancement to Chien et al. scheme. However, their scheme has many security flaws. This paper points out weaknesses of Liu et al. scheme and presents an enhancement to conquer the weaknesses.