Global Mobility Networks(GLOMONETs) in wireless communication permits the global roaming services that enable a user to leverage the mobile services in any foreign country. Technological growth in wireless communication is also accompanied by new security threats and challenges. A threat-proof authentication protocol in wireless communication may overcome the security flaws by allowing only legitimate users to access a particular service. Recently, Lee et al. found Mun et al. scheme vulnerable to different attacks and proposed an advanced secure scheme to overcome the security flaws. However, this article points out that Lee et al. scheme lacks user anonymity, inefficient user authentication, vulnerable to replay and DoS attacks and Lack of local password verification. Furthermore, this article presents a more robust anonymous authentication scheme to handle the threats and challenges found in Lee et al.'s protocol. The proposed protocol is formally verified with an automated tool(ProVerif). The proposed protocol has superior efficiency in comparison to the existing protocols.