Relying on amicable orthogonal design, we develop for multiple-antenna systems a General differential space-time block code (GDSTBC), which imposes no restrictions on underlying signal constellation compared with the existing differential space-time designs. 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 Noncoherent decoder (NCD) for fiat Rayleigh fading channels. We show that NCD may recover data symbols with full antenna diversity and linear complexity at high signal-to-noise ratio. Particularly, while three kinds of conventional signal constellations are used in GDSTBC, we derive the simplified versions of NCDs which can effectively reduce the cost of implementation.