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In this paper, an iterative multiple symbol differential detection (MSDD) for turbo coded differential unitary space-time modulation (DUSTM) is developed by using an a posteriori probability (APP) demodulator under correlated slow and fast Rayleigh flat fading channels. The metric function necessary for the detection operates based on linear prediction. Two approaches are presented to utilize the metric. In the first approach, the BCJR algorithm is modified to deal with the increased-state trellis of the differential modulation. In the second approach, the VA is modified to find the symbol sequences associated with the survivors for the BCJR algorithm.