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We propose a scheme of utilizing multilevel space-time signal-based turbo code (MST-SB-TC) for wireless communication systems with multiple antennas over very rapidly Rayleigh block fading channels where the fading coefficients changes independently for every transmitted signal. No channel state information (CSI) is available and even unitary space-time signals fail to operate. We give an effective method which applies MST-SB-TC as an alternative to the original multilevel space-time modulation and present an effective multilevel space-time (UST) signal-based BCJR-like maximum a posteriori (MAP) decoding algorithm, which makes full use of the channel characteristics when calculating the branch metrics. With iterative decoding and/or multiple receive antennas, it can further improve the system performance, which helps to give an acceptable bit error rate.