Remote user authentication is desirable for a Telecare Medicine Information System (TMIS) for the safety, security and integrity of transmitted data over the public channel. In 2013, Tan presented a biometric based remote user authentication scheme and claimed that his scheme is secure. Recently, Yan et al. demonstrated some drawbacks in Tan's scheme and proposed an improved scheme to erase the drawbacks of Tan's scheme. We analyze Yan et al.'s scheme and identify that their scheme is vulnerable to off-line password guessing attack, and does not protect anonymity. Moreover, in their scheme, login and password change phases are inefficient to identify the correctness of input where inefficiency in password change phase can cause denial of service attack. Further, we design an improved scheme for TMIS with the aim to eliminate the drawbacks of Yan et al.'s scheme.