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Differential unitary space-time modulation has been proposed recently in the literature for multiple-antenna systems over Rayleigh fading channels, where neither the transmitter nor the receiver knows the fading coefficients. For the success of differential unitary space-time modulation, it is important to design unitary space-time signal constellations with large diversity product which is a primary property for the signal constellations to have good performance in high signal-to-noise ration (SNR) scenarios. In this paper, a new method is presented to design signal constellations for differential unitary space-time modulation. A full-rotation matrix is introduced in the proposed method to design non-group constellations with larger diversity product than that of cyclic group codes. Simplification has also been made to the proposed method to minimize the computational complexity. Simulation results show that the proposed signal constellations perform better than the cyclic codes under high SNR.