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This paper presents a natural concatenation between the real or complex square orthogonal designs and the differential unitary space-time modulation scheme for multiple transmit antennas. This concatenation renders the differential unitary space-time demodulator to detect in a decoupled way the information symbols and hence to have a very low decoding complexity. This fast differential demodulation method for multiple transmit antennas can be regarded as a generalization of the existing differential detection method proposed by Tarokh and Jafarkhani for two and four transmit antennas based on orthogonal designs. By using a systematic matrix-vector representation, a unified and simplified form of differential unitary demodulation via square orthogonal designs for any number of transmit antennas and any transmission rate in bits per channel use is provided.