The anonymity, mutual authentication and low computation cost are the three important requirements for authentication of global mobility networks (GLOMONETs). Based on these three requirements, many authentication schemes have been proposed. In [9], an enhanced authentication scheme called Enhanced Authentication with Anonymity for Roaming Service (EAARS) has been proposed and it is claimed that the scheme can guarantee anonymity of mobile users and establish a secure session key for mobile users. In this paper, we discover that the scheme cannot provide user anonymity against malicious mobile users as claimed. We analyze the vulnerabilities of the EAARS scheme and propose an improved authentication scheme. The proposed scheme can not only keep the merits of the EAARS scheme, but also provide user anonymity and avoids session key compromise. Our numerical results by Colored Petri Nets (CPN) modeling show that our proposed scheme is more secure with ability to avoid these threats.