In 2005,Liu et al.proposed an improvement to Chien et al.’s remote user authentication scheme,using smart cards,to prevent parallel session attack.This article,however,will demonstrate that Liu et al.’s scheme is vulnerable to masquerading server attack and has the system’s secret key forward secrecy problem.Therefore,an improved scheme with better security strength,by using counters instead of timestamps,is proposed.The proposed scheme does not only achieve their scheme’s advantages,but also enhances its security by withstanding the weaknesses just mentioned. In 2005, Liu et al .proposed an improvement to Chien et al.’s remote user authentication scheme, using smart cards, to prevent parallel session attack. This article, however, will demonstrate that Liu et al.’s scheme is vulnerable to masquerading server attack and has the system’s secret key forward secrecy problem.Therefore, an improved scheme with better security strength, by using counters instead of timestamps, is proposed.The proposed scheme does not only achieve their scheme’s advantages, but also enhances its security by withstanding the weaknesses just mentioned.