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A novel technique is presented for the construction of full-rate, full-diversity space-time block codes (STBCs) from orthogonal STBCs (OSTBCs), having empty slots left in their codeword matrices for orthogonality. Two new STBCs are obtained, which are both full-rate and full-diversity, for three and four transmit antennas. The higher decoding complexity of these structures is reduced owing to non-orthogonality by using a conditional maximum-likelihood decoder. The new optimised codes provide better error performance than their full-rate full-diversity counterparts given in the literature.