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Per-flow unfairness of TCP throughput in the IEEE 802.11 wireless LAN environment has been reported. Although a number of researchers have proposed various methods for alleviating the unfairness, they evaluated the fairness of their methods separately from the network bandwidth utilization, meaning that they did not consider the trade-off relationships between fairness and bandwidth utilization. In this paper, we first propose a novel performance metric considering both per-flow fairness and bandwidth utilization at network bottlenecks. We then propose a transport-layer solution for alleviating TCP unfairness. We finally evaluate the performance of the proposed method through experiments in a real wireless LAN environment. We demonstrate that the proposed method can achieve better a trade-off between fairness and throughput, regardless of vendor implementations of wireless access points and wireless interface cards.