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This paper introduces a space-time decision feedback equalizer whose coefficients are recursively renewed on the basis of the modified affine projection algorithm (APA). Despite its effectiveness against a rank-deficiency problem, the complexity of the conventional APA utilizing the sample matrix inversion is considerable. Furthermore, the shift invariance property could not be exploited in the case of a space-time decision-directed equalizer (STDE) application. To overcome such challenges, this paper introduces an APA employing a hyperplane projection scheme to reduce computational complexity without any degradation in its convergence characteristic and tracking capability. The performance of the proposed equalization methodology is verified by showing its superior bit error rate behaviors, fast convergence property, and reduced computational complexity by performing adaptive STDE under the single-input-multiple-output wireless multipath fading channel.