In this paper, the application of space time trellis codes to multiband orthogonal frequency division multiplexing ultra-wideband (MB-OFDM UWB) systems is investigated. We propose a coding scheme that could fully exploit all the available channel diversity, including space diversity, frequency diversity and inter-subband diversity. Performance of the proposed system is compared with that of the conventional MB-OFDM UWB system in terms of frame error rate (FER). Simulation results show that this system outperforms the conventional one. As an example, an improvement of at least 5 dB at FER=1E-2 could be achieved over the IEEE 802.15.3a channel modes of CM1 and CM2 in the system equipped with only two transmit antennas and one receive antenna. Moreover, the system performance could be further improved when the number of antennas and/or the number of trellis states is increased.