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In this letter, we derive the optimal detector for the so-called spatial modulation (SM) system introduced by Mesleh et al. in (Mesleh, 2006). The new detector performs significantly better than the original (~ 4 dB gain), and we support our results by deriving a closed form expression for the average bit error probability. As well, we show that SM with the optimal detector achieves performance gains (~ 1.5 - 3 dB) over popular multiple antenna systems, making it an excellent candidate for future wireless communication standards.