Remote user authentication is used to validate the legitimacy of a remote login user. Conventional user authentication schemes are suited to solve the privacy and security problems for the single client/server architecture environment. However, the use of computer networks and information technology has grown spectacularly. More and more network architectures are used in multi-server environments. In this paper, we propose a new remote user authentication scheme. The scheme can be used in multi-server environments. In our scheme, the system does not need to maintain any verification table, and the users who have registered in the servers do not need to remember different login passwords for various servers. In addition, our scheme can also withstand replay and modification attacks. Furthermore, it allows users to choose their passwords freely, and a user can be removed from the system easily when the subscription expires.