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We address the problem of frequency reuse schemes in the downlink of the fixed two-hop orthogonal frequency division multiple access (OFDMA) cellular relaying networks. There has been little work on specific frequency reuse schemes for this system in the literatures, although this is the key element for realizing the potential capacity and coverage increase offered by the relay. Therefore, we propose a novel frequency reuse scheme for spectrum efficiency enhancement. Based on this scheme, inter-cell interference (ICI) and SINR received by one- hop and two-hop users are analyzed. System-level simulation results show that our presented frequency reuse scheme can achieve significant improvement on spectrum efficiency compared to modified soft frequency reuse (MSFR) scheme.