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We propose a scheme of utilizing unitary space-time symbol based nonbinary turbo code (USTSBTC) for wireless communication systems with multiple antennas over extremely fast Rayleigh block fading channels, where no channel state information (CSI) is available. We give an effective way of applying USTSBTC as an alternative to the original unitary space-time modulation and present an effective unitary space-time (UST) symbol based BCJR-like maximum a posteriori (MAP) decoding algorithm, which can greatly improve the system performance. Since a constellation with a small size of T can also works well for a long coherence interval, our scheme fits for more conditions. With iterative decoding and/or multi-antennas, it can further improve the system performance, which helps to give an acceptable bit error rate. Specially, we demonstrate for the first time by simulations that when combined with a powerful error correcting code, transmit diversity would be more effective when a very low bit error rate is needed.