The spatial modulation (SM) divides input data into antenna indexes and data symbols, and transmits data symbols via the specific antenna chosen by the antenna index. Soft decision technology for the SM system has not been developed, and there is room for improving the receive performance. In this paper, soft-output maximum likelihood (ML) detector for antenna index and data bit is derived to recover the desired signals by soft decision. Simulation results show that the conventional SM system with hard decision has a limitation in its performance as compared to SIMO (single-input multiple-output) system. On the other hand, the proposed SM with soft decision outperforms the SM with ML detector based on hard decision.