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In this paper, we analyze the performance of the differential space-time modulation (DSTM) in Rayleigh fading channels. By using the moment-generating function (MGF)-based approach, we derive a number of closed-form expressions for the pairwise error probability (PEP) of the DSTM in various fading environments. For spatially independent channels, we derive a closed-form expression for the exact PEP of the DSTM for both slow- and fast-fading cases. In the case of fast-fading channels, we show that an irreducible error floor exists in the PEP and in the block error rate of the DSTM, and derive a closed-form expression for the PEP error floor in terms of the fading rate. For spatially correlated channels, we derive a new closed-form expression for the PEP at asymptotically high signal-to-noise ratios and show that an existing asymptotic PEP expression derived by the residue method can also be obtained by using the MGF-based approach. Finally, we use computer simulations to verify the theoretical results.