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Most space-time codes in the literature were proposed based on two ideal channel conditions: either quasistatic or rapid fading. However, these codes may suffer performance degradation due to temporal correlation caused by the movement of the mobile terminal or imperfect interleaving. In this correspondence, we provide a novel analytical framework for the diversity analysis of space-time modulation in time-correlated fading environment. We show that the space-time signals of square size achieving full diversity in quasistatic fading channels also achieve full diversity in time-correlated fading channels, independently of the time correlation matrix. Consequently, various classes of space-time signals designed for quasistatic fading channels can also be used for full-diversity transmission over time-correlated fading channels. Moreover, we show that if the time correlation matrix is of full rank, the design criteria for time-correlated fading channels are the same as those for rapid fading channels. To illustrate the theoretical results, some simulations were also performed under various temporal fading conditions.