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To enhance the usage of radio spectrum, a wireless network, named as the cognitive wireless network, which allows the unlicensed users to scan and use idle radio spectrum, has attracted a lot of attention recently. Because the radio spectrum has to return to the licensed user whenever the licensed user needs it, the radio spectrum of cognitive wireless networks is a precious resource. Hence, how to avoid collisions and enhance the throughput of the network are important issues for designing MAC protocols of cognitive wireless networks. In this paper, we propose an efficient dynamic adjusting MAC (EDA-MAC) protocol for cognitive wireless networks. EDA-MAC is improved from C-MAC, which assigns each joined host a dedicated beacon slot and thus it has a good potential to avoid contentions and collisions and achieve high throughput. The improvements we made are listed as follows: First, instead of a fixed number of signaling slots of C-MAC, EDA-MAC dynamically adjusts the number of signaling slots according to the number of estimated contenders and thus reduces the number of collisions and shortens the join process. Second, each joined host can inform others its transmission intention by its beacon frame. Since each joined host has a dedicated beacon slot, almost all the beacon frames can be sent without any collision. Third, each communication group contains a leader. The leader is responsible for coordinating the join process, data transmission, transmission rate selection, channel scan, and channel switch of each host in the communication group. With the coordination of the leader, unnecessary contentions and collisions can be avoided and thus enhances the throughput of the network. Simulation results justify the efficiency of the proposed EDA-MAC protocol.