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The medium access control (MAC) protocol through which mobile nodes can share a common broadcast channel is essential in ad hoc networks. Due to the existence of hidden terminals and multihop feature of ad hoc networks, contention among nodes is not homogeneous. Some nodes are at a disadvantage in access to the shared channel and suffer severe throughput degradation when load to channel is high. This is known as the "fairness problem". A new simple yet effective queue backoff fair algorithm is proposed. To quantify the degree of the fairness effect of the algorithm, an improved fairness index (IFI) is also defined. Based on IFI, the goal of achieving channel access fairness relative to effective aggregate throughput becomes equivalent to minimizing the improved fairness index. Analysis and simulation results show that, by choosing appropriate parameters, the new algorithm achieve lower improved fairness index and consequently improve the fairness relative to effective aggregate throughput, compared with the IEEE 802.11 binary exponential backoff (BEB) algorithm and other algorithms.