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In this paper, we propose an amicable-orthogonal-design-based differential space-time block code (ADSTBC) for multiple antennas. Compared with the existing differential space-time designs, our scheme imposes no restrictions on underlying signal constellation. This generalization potentially allows the spectral efficiency to be increased by carrying information not only on phases but also on amplitudes. We then derive a coherent decoder and a noncoherent decoder (NCD) for flat Rayleigh fading channels. As a result of amicable orthogonal design, ADSTBC is shown capable of recovering data symbols with linear complexity and full antenna diversity at high signal-noise-ratio, no matter whether channel estimates are available at the receiver. Particularly, while the PSK constellation is used in ADSTBC, we will prove that the performance of differential detection is about 3dB worse than that of coherent decoding.