In this paper, we mathematically derive a matrix-form solution named resource allocation matrix (RAM) for sub-band allocation in an orthogonal frequency division multiple access (OFDMA) system. The proposed scheme is designed to enhance throughput under a strict user fairness condition such that every user has an equal number of sub-bands per frame. The RAM designates the most preferable sub-band for every user. The proposed scheme is evaluated in terms of throughput and user fairness by comparison with the proportional fairness (PF) scheme and greedy scheme. Numerical results show that the proposed scheme has overwhelming superiority to other schemes in terms of fairness and tight competitive in terms of throughput.