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One major assumption in all space-time block coding (STBC) schemes is that the channel remains static over the length of the codeword. However, time selective fading channels do exist, and in such case the conventional STBC detectors can suffer from a large error floor in the high signal-to-noise ratio cases. As a sequel to our previous papers on this subject, this paper aims to eliminate the error floor of the Hi coded STBC systems (i = 3 and 4) by employing the technique of parallel interference cancellation (PIC). Compared with the conventional Hi detector, the PlC detector incurs a moderately higher computational complexity, but this can be justified by the enormous performance improvement.