Multiple-symbol detection (MSD) of differential unitary space-time modulation (DUSTM) uses maximum likelihood sequence detection of mu symbols to achieve a performance gain over conventional 2 symbol differential detection (DD). Using results from MSD, an additive symbol by symbol metric is developed for noncoherent detection of trellis-coded DUSTM (TC-DUSTM). In the Rayleigh fading channel, performance is almost as good as the performance of coherent detection of TC-DUSTM when mu is large, while computational complexity increases only linearly with the size of mu.