Networks are trending towards wireless systems that provide support for mobile computing. The Byzantine Agreement (BA) protocols used in static networks do not perform well in a dynamically changing mobile environment. Mobile commerce and related applications are necessary for wireless networks. There are numerous properties in a wireless network that play important roles. For example, the processors in a wireless network have highly mobile capabilities. Processors can immigrate into or move away from the network at any time. Although mobile technology has brought greater convenience, it is comparatively more dangerous. Wireless systems are susceptible to security flaws such as attacks by hackers. The number of allowable faulty components within the system is also decreased. To increase the number of allowable faulty components and ensure network security, a simple, secure and efficient protocol, BAM, is proposed to handle the BA problem. The fault symptoms include malicious and dormant faults. Furthermore, the proposed protocol uses the minimum number of message exchange rounds to make all healthy processors agree on a common value and can tolerate the maximum number of allowable faulty components. The proposed method will also ensure message security and increase the system's fault tolerant capability.