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In this paper, a novel noncoherent detection algorithm for differential space-time modulation (DSTM) over flat-fading multiple-input-multiple-output channels is presented. This algorithm, which is referred to as decision-feedback subset multiple-symbol differential detection (DF-S-MSDD), combines ideas from decision-feedback differential detection (DFDD) and subset multiple-symbol differential detection (S-MSDD). More specifically, the DF-S-MSDD decision metric includes a number of previous decisions (i.e., decision feedback), and the optimization over the remaining hypothetical symbols returns decisions only on a subset of these symbols (i.e., S-MSDD). Furthermore, an implementation of DF-S-MSDD based on tree-search (TS) methods is devised. Due to the concept of subset detection, DF-S-MSDD outperforms MSDD in terms of error-rate performance. At the same time, due to the use of decision feedback, it also requires lower computational complexity than the TS-based MSDD schemes for the DSTM recently proposed in the literature.