An ordered successive interference cancellation (OSIC) scheme based on combined post-processing signal-to-interference-plus-noise ratio (PSINR) is proposed for multiple-input multiple-output (MIMO) systems with retransmission. For the OSIC procedures at the current transmission round, instead of reusing the PSINRs and decision statistics calculated for the previous transmission rounds, the proposed OSIC scheme newly calculates the combined PSINRs and combined decision statistics from the available receive signal vectors and channel matrices at every retransmission. Therefore, the proposed OSIC scheme utilizes all receive signal vectors and channel matrices obtained up to the current transmission round during the OSIC procedures. A low-complexity version of the proposed OSIC scheme is also proposed, and the low-complexity version recalculates the combined PSINRs and combined decision statistics from part of the available receive signal vectors and channel matrices. Simulation results verify that the proposed schemes achieve significantly better error performance than existing OSIC schemes based on the detection and combining process for MIMO systems with retransmission.