Abstract: Construction of a BCM code on the Rayleigh-fading channel can be realized by combining component codes, whose minimum product distance and Hamming distance are as large as possible, with set partitioning method proposed by Ungerboeck. However, using this mapping method, the complexity of a BCM code constructed is greatly increased, which makes a degradation of the whole performance. In the paper, a new set partitioning method is proposed. Simulation result shows that BCM codes constructed by this mapping method have a better performance than those constructed by using Ungerboeck set partitioning mapping.