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Frequency reuse among relay stations (RSs) in a down- link access zone is widely adopted for throughput enhancement in IEEE 802.16j relay networks. Since the areas covered by the RSs or the base station (BS) may overlap, some mobile stations (MSs) at the border between two neighboring transmitting stations (RS or BS) using an identical frequency band may suffer severe interference or outage. This co-channel interference within the cell degrades the quality of service (QoS) fairness among the MSs as well as the system throughput. Exclusive use of a frequency band division (orthogonal resource allocation) among RSs can solve this problem but would cause degradation of the system throughput. We observe a trade-off between system through- put and QoS fairness in the previously reported schemes based on frequency reuse. In this paper, we propose a new frequency reuse scheme that achieves high system throughput with a high fairness level in QoS, positioning our scheme far above the trade-off curve formed by previous schemes. We claim that our scheme is beneficial for applications in which a high QoS level is required even for the MSs at the border. Exploiting the features of a directional antenna in the BS, we create a new zone in the frame structure. In the new zone, the RSs can serve the subordinate MSs at the border and prone to interference. In a 3-RS topology, where the RSs are located at points 120° apart from one another, the throughput and Jain fairness index are 10.64 Mbps and 0.62, respectively. On the other hand, the throughput for the previously reported overlapped and orthogonal allocation schemes is 8.22 Mbps (fairness: 0.48) and 3.99 Mbps (fairness: 0.80), respectively. For a 6-RS topology, our scheme achieves a throughput of 18.38 Mbps with a fairness of 0.68; however, previous schemes with frequency reuse factors of 1, 2, 3, and 6 achieve a throughput of 15.24 Mbps (fairness: 0.53), 12.42 Mbps (fairness: 0.71), 8.84 Mbps (fairness: 0.88), and 4.5- Mbps (fairness: 0.88), respectively.