In this paper, the authors focus on resource block allocation issue in the downlink transmission systems of the Long Term Evolution (LTE). In existing LTE standards, all Allocation Units (AUs) allocated to any user must adopt the same Modulation and Coding Scheme (MCS), which is determined by the AU with the worst channel condition. Despite its simplicity, this strategy incurs significant performance degradation since the achievable system throughput is limited by the AUs having the worst channel quality. To address this issue, a two-step resource block allocation algorithm is proposed in this paper.