Smart card has been adopted to various applications. In 2000, Hwang and Li proposed a remote user authentication scheme, which is also using smart card. Nine months later, Chan and Cheng pointed out that there is a weakness in the remote authentication scheme proposed by Hwang and Li. In this paper, we show that Chan and Cheng's attack does not work well because they did not consider the format of user's identity. In addition, we propose several ways to solve the problem of Chan and Cheng's attack.