Authentication schemes preserving user anonymity have first been proposed by Das et al, and most of user anonymity schemes provide user anonymity against outside attacks in the communication channel. In this paper, according to the increasing of personal information exposure incidents by server attack, we propose a new authentication scheme that provides user anonymity against server as well as one against outside attacks in the communication channel. Furthermore, the proposed authentication scheme provides traceability that remote server should be able to trace the malicious user and it also solves the problem of increasing computational load of remote server by solving weakness of wrong password input by mistake.