The security for Telecare Medicine Information Systems (TMIS) has been crucial for reliable dispensing of the medical services to patients at distant locations. Security and privacy element needs to be there for any physician or caregiver to make certain an appropriate diagnosis, medical treatment or any other exchange of critical information. In this connection, many relevant TMIS-based authentication schemes have been presented, however various forms of attacks and inefficiencies render these schemes inapplicable for a practical scenario. Lately, Amin et al. proposed a scheme based on a multi-server authentication for TMIS. However, the Amin et al., scheme has been found vulnerable to user and server impersonation attacks. We have proposed an improved model with higher performance and efficiency, as evident from the forthcoming sections. Besides, the scheme has been backed up by formal security analysis using BAN logic to ensure the resilience of the proposed scheme.