Remote user authentication is essential in network environment to protect unauthorized access of a networked system. Over the past years, many remote user authentication schemes have been put forth. In 2003, to prevent from forgery attacks encountered in Hwang-Li's scheme, a modified remote user authentication scheme was proposed by Shen, Lin and Hwang. However, Leung, Chang, Fong and Chen showed the modified scheme is still insecure. Therefore, in the paper, we would like to improve Shen et al. scheme and propose another secure remote user authentication scheme from bilinear pairings