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A novel method to significantly reduce the complexity of real-time hardware/software implementations of MSGRbased matrix inversion for MIMO wireless communication systems is presented. It is shown, through extensive simulation of this new technique within a T-BLAST MIMO system, that removing the scale-factor from the MSGR algorithm has no adverse effect on the bit-error rate performance of this practical application. Moreover, this new modification to the MSGR algorithm reduces the number of multiply and divide operations in MSGR-based matrix inversion by 18-19%. Furthermore, it is shown that reduced-precision fixed-point arithmetic may be exploited to further reduce the complexity of the implementation while maintaining acceptable bit-error rate performance.