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This paper proposes a space-time-frequency coding scheme for MIMO-OFDM that achieves full rate for an arbitrary number of antennas with complex-valued information symbols. In addition, the proposed scheme provides a very high level of diversity with relatively low complexity. In the new scheme, the spatial and frequency spreading is followed by a temporal spreading that facilitates simple separation of the respective signals sent by the various transmit antennas. This temporal spreading enables perfect separation of the superimposed transmit signals at the receiver prior to channel estimation. The Local Maximum Likelihood (LML) method of Rugini et al is employed to further reduce complexity. Simulations are presented demonstrating the efficacy of the new scheme. For example, for cases where an Orthogonal Space-Time Block (OSTBC) code exists, the new scheme is shown to provide the same full-diversity as the OSTBC. Again, though, the new scheme is applicable for an arbitrary number of transmit antennas and complex-symbol constellations.