Iterative detection and decoding based on a soft interference cancellation–minimum mean squared error (SIC-MMSE) scheme provides efficient performance for coded MIMO systems. The critical computational burden for a SIC-MMSE detector in a MIMO system lies in the multiple inverse operations of the complex matrix. In this paper, we present a new method to reduce the complexity of the SIC-MMSE scheme based on a MIMO detection scheme that uses a single universal matrix with a non-layer-dependent inversion process. We apply the Taylor series expansion approach and derive a simple non-layer-dependent inverse matrix. The simulation results reveal that the utilization of the universal matrices presented in this paper produces almost the same performance as the conventional SIC-MMSE scheme but with low computational complexity.