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We propose a new class of unitary subgroups which is suitable to make differential unitary space-time codes for fast fading channels. These subgroups are derived from a double coset decomposition of unitary groups called Bruhat decomposition. We give some examples of the proposed unitary subgroup space-time codes for phase-shift keying (PSK), and display the performance for Rayleigh-fading channels. Finally, we describe how the new space-time codes are combined with coded modulation systems.