In this paper, we propose a new resource allocation scheme for an OFDMA relay network with multicells. In the proposed scheme, by sharing the channel state information (CSI) between base stations, resources are allocated to users and relays to maximize the overall sum of the achievable rate under fairness constraints. In order to reduce the computational complexity, a resource allocation scheme is proposed by separating subcarrier allocation and power allocation into two parts. First of all, by considering inter-cell interference (ICI), a subcarrier is allocated to a user-relay pair, and power is allocated relays. Simulation results show that the proposed scheme achieves higher spectral efficiency per subcarrier than the static scheme and reduces the outage probability compared to the static and greedy schemes.