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This paper proposes a novel medium access control (MAC) scheme for multichannel cognitive radio (CR) ad hoc networks, which achieves high throughput of CR system while protecting primary users (PUs) effectively. In designing the MAC scheme, we consider that the PU signal may cover only a part of the network and the nodes can have the different sensing result for the same PU even on the same channel. By allowing the nodes to use the channel on which the PU exists as long as their transmissions do not disturb the PU, the proposed MAC scheme fully utilizes the spectrum access opportunity. To mitigate the hidden PU problem inherent to multichannel CR networks where the PU signal is detectable only to some nodes, the proposed MAC scheme adjusts the sensing priorities of channels at each node with the PU detection information of other nodes and also limits the transmission power of a CR node to the maximum allowable power for guaranteeing the quality of service requirement of PU. The performance of the proposed MAC scheme is evaluated by using simulation. The simulation results show that the CR system with the proposed MAC accomplishes good performance in throughput and packet delay, while protecting PUs properly.