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In this paper, a novel hierarchical algorithm is proposed for orthogonal frequency-division multiple-access wireless mesh networks (WMNs). The problem is to maximize the overall end-to-end rate with balancing the fairness among users, and find a new method as a substitute for Lee's resource allocation algorithm with high computational complexity. The proposed algorithm consists of two subproblems, where the mesh router (MR) allocates groups of subcarriers to the mesh clients (MCs) based on Nash bargaining solution according to the limited information, and each MC allocates subcarriers to each of its outgoing links based on the equal power allocation according to the full information of channel gains. The simulation results demonstrate that the proposed algorithm have a comparable overall end-to-end rate with the maximal rate algorithm. Moreover, compared to Lee's resource allocation algorithm, the proposed algorithm not only needs lower computational complexity, but also provides comparable fair opportunities for the respective users (MCs), and a comparable end-to-end rate of each user.