The Mobile WiMAX IEEE 802.16e is a new technology supporting broadband wireless communication with fixed and mobile access. The standard offers high throughput broadband connections, supporting handover and roaming capabilities, and provides a security sub layer, which is responsible for secrecy, authentication and secure key exchange. In the area of security aspects, Mobile WiMAX exhibits vulnerabilities while adopting improved security architecture. Several versions of 802.16 networks were released. While the first versions have shown some security weaknesses that were later corrected by the recently released versions, the security mechanisms of 802.16 still remain vulnerable and the limited deployment of such technology is insufficient to satisfy the demands of security. This paper focuses on reducing the security vulnerabilities in the authorization protocol PKM and the generation of traffic encryption keys (TEKs). We propose the usage of 1. A formal analysis of the PKM protocol (authorization phase and exchange of TEKs phase) and 2.Device certificate for key exchange process to provide secure authentication and 3. Give a formal analysis of our new PKM protocol (authorization phase and exchange of TEKs phase). The formal analysis has been conducted using a specialized model checker Scyther, which provides formal proofs of the security protocol. The revised authentication protocol is expected to provide better secure platform for all process of PKM.