Base station coordination is considered as a promising technique to mitigate inter-cell interference and improve the cell-edge performance in cellular orthogonal frequency division multiple-access (OFDMA) networks. The problem to design an efficient radio resource allocation scheme for coordinated cellular OFDMA networks incorporating base station coordination has been only partially investigated. In this contribution, a novel radio resource allocation algorithm with universal frequency reuse is proposed to support base station coordinated transmission. Firstly, with the assumption of global coordination between all base station sectors in the network, a coordinated subchannel assignment algorithm is proposed. Then, by dividing the entire network into a number of disjoint coordinated clusters of base station sectors, a reduced-feedback algorithm for subchannel assignment is proposed for practical use. The utility function based on the user average throughput is used to balance the efficiency and fairness of wireless resource allocation. System level simulation results demonstrate that the reduced-feedback subchannel assignment algorithm significantly improves the cell-edge average throughput and the fairness index of users in the network, with acceptable degradation of cell-average performance.