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In this letter, a new constellation design for differential unitary space-time modulation is proposed. We generate a set of unitary matrices from the multiplication of a simple unitary matrix with entries of ± 1 by diagonal matrices made from quaternary alphabets. Then, the constellation is formed from the product of the optimum matrix chosen from this set and the optimized diagonal matrix first used for the cyclic codes. We show that, without deteriorating the transmission rate, the proposed constellation yields a larger diversity product as well as a lower union bound for pairwise error probability with the same or a lower complexity compared to other previously proposed constellations.