Telecare medical information systems (TMISs) are increasingly popular technologies for healthcare applications. Using TMISs, physicians and caregivers can monitor the vital signs of patients remotely. Since the database of TMISs stores patients' electronic medical records (EMRs), only authorized users should be granted the access to this information for the privacy concern. To keep the user anonymity, recently, Chen et al. proposed a dynamic ID-based authentication scheme for telecare medical information system. They claimed that their scheme is more secure and robust for use in a TMIS. However, we will demonstrate that their scheme fails to satisfy the user anonymity due to the dictionary attacks. It is also possible to derive a user password in case of smart card loss attacks. Additionally, an improved scheme eliminating these weaknesses is also presented.