Wireless Local Area Networks WLAN based on wireless technology, i.e., no physically connection exists. Therefore, security is always a major concern for WLAN development and one of the major problems in WLAN security issue is authentication. EAP (Extensible Authentication Protocol) is a framework of authentication that uses several methods of authentication such as TLS, TTLS, PEAP and LEAP. EAP-LEAP (EAP-Lightweight Extensible Authentication Protocol) is widely used in WLAN (Wi- Fi /802.11 and Wi-MAX/802.16) as solution of authentication problem. This paper presents an assessment to the security of EAP-LEAP in details and explores many weakness points. As a solution to the presented flaws, we present a new proposal EAP- MEAP in details to overcome these shortage points. Finally we present an security assessment to our proposed protocol compared with EAP-LEAP.