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In this paper, we propose the trellis coded differential unitary space-time modulation (TC-DUSTM) and present the derivation of the formulae of the pairwise error-event probability (PEP) and the bit error probability (BEP) for this scheme. We found that in a multi-input multi-output (MIMO) system with M transmit and N receive antennas, apart from the diversity gain of MN, a coding gain of lmin is also obtained for the TC-DUSTM, where lmin is the length of the shortest error event. Additional coding gain comes from the product of the dissimilarities along the path of the shortest error event. These performance analyses suggest design criteria for the TC-DUSTM to obtain a best BEP performance. Through simulations we show that these analyses are accurate, especially at high signal-to-noise ratio (SNR).