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This paper proposes a new dynamic spectrum access (DSA) algorithm for cognitive radio networks. Once initialized, this algorithm works without the need of coordination overhead and hence can be used when no control channel is available. Secondary user (SU) lists and predetermined access control are used in this algorithm. We analyze the probability of no SU collision with primary user and the throughput of our proposed algorithm. Extensive simulations show that our algorithm outperforms the existing DSA algorithm in terms of both the aggregate throughput and the traffic distribution fairness. Furthermore, the validity of our analysis is confirmed by simulation results.