In multi-cell OFDMA-based networks, co-channel interference (CCI) is inevitable when the frequency reuse scheme is used. The CCI affects the performance of users, especially that of cell edge users. Several frequency reuse schemes and subcarrier allocation algorithms have been proposed to solve the CCI problem. Nevertheless, it is difficult to improve both the cell capacity and the performance of cell edge users since they have a trade-off. In this paper, we propose a new balanced frequency reuse (BFR) as a new frequency partitioning scheme that gives more power to the users in the outer region and allocates more subcarriers to the users in the inner region. In addition, we propose ordering and directional subcarrier allocation (ODSA) for our frequency partitioning proposal to mitigate the CCI effectively when cells have heterogeneous traffic loads. The performance of the proposed BFR with the ODSA algorithm is investigated via analyses and simulations. Performance evaluation shows that the proposed BFR with the ODSA algorithm can increase both the spectral efficiency and the performance of cell edge users if the transmission power is appropriately handled.