In this paper, the issue of blind detection of Alamouti-type differential space-time (ST) ${pi}/2$-shifted BPSK modulation in static Rayleigh fading channels is considered. We introduce a novel transformation to the received signal from each receiver antenna such that this binary ST modulation, which has a second-order transmit-diversity, is equivalent to QPSK modulation with second-order receive-diversity. The pre-detection combining of the result of transformation allows us to apply a low complexity detection technique specifically designed for receive-diversity, namely, scalar multiple-symbol differential detection (MSDD). With receiver complexity proportional to the observation window length, our receiver can achieve the performance 1.5dB better than that of conventional differential detection ST and 0.5dB worse than that qf a coherent maximum ratio combining receiver (with differential decoding) approximately.