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In this paper, we present a class of unitary signal constellations used for differential space-time modulation with two transmit antennas. The proposed signal constellations improve the cyclic group codes. In particular, the 16 signal constellation in the class has the largest known diversity product of 4/spl radic/2/2 among all the existing unitary space-time codes. Furthermore, the 16 signal constellation is a subset of a finite group of size 32, which consists of the original 16 unitary matrices V/sub l/, l=0, 1, ..., 15, and their multiplications with j=/spl radic/(-1), i.e., jV/sub l/, l=0, 1, ..., 15.