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Unitary (USTM) has got more attention for its potential in implementing high data rate transmission in a noncoherent multiple-antenna Rayleigh flat fading channel. In this paper, we have given out a bandwidth efficient turbo trellis-coded modulation scheme for the non-coherent multiple-antenna Rayleigh fading channel, where the channel state information (CSI) is not necessary both at the transmitter and the receiver. In this proposal, we combine USTM as constellations with the turbo trellis-coded modulation, resulting in the turbo trellis-coded USTM (TTC-USTM), with the trellis-coded USTM encoder as the component encoders. We have also applied the iterative maximum a posteriori (MAP) algorithm. According to PC simulations, we demonstrated that without bandwidth expansion, TTC-USTM produces obvious coding gains over its uncoded counterparts.