In this paper, we address fault-diagnosis agreement (FDA) problems in distributed wireless networks (DWNs) with arbitrary fallible nodes and healthy access points. We propose a new algorithm to reach an agreement among fault-free members about the faulty ones. The algorithm is designed for fully connected DWN and can also be easily adapted to partially connected networks. Our contribution is to reduce the bit complexity of the Byzantine agreement process by detecting the same list of faulty units in all fault-free members. Therefore, the malicious units can be removed from other consensus processes. Also, each healthy unit detects a local list of malicious units, which results in lower packet transmissions in the network. Our proposed algorithm solves FDA problems in 2t+1 rounds of packet transmissions, and the bit complexity in each wireless node isO(nt+1).