Differential space-time modulation (DSTM) is an encoding technique for multiantenna systems that allows the receiver to detect the transmitted signals without the knowledge of the fading channels. It can be viewed as an extension of the differential phase-shift keying (DPSK) scheme in single antenna systems. In this paper, the performance of the DSTM is analyzed. By using the moment-generating function-based approach, a closed-form expression for the exact pairwise error probability (PEP) of the DSTM in spatially independent time-varying Rayleigh fading channels is derived. It is shown that the DSTM exhibits an irreducible error rate and a closed-form expression for this error floor in terms of the fading rate is presented. As a byproduct, an exact PEP expression of the DSTM in spatially independent quasi-static fading channels is also obtained.