In a multi-user multiple-input multiple-output (MU-MIMO) system that adopts zero-forcing (ZF) as a precoder, the best selection is the combination of users who provide the smallest trace of the inverse of the channel auto-correlation matrix. Noting that the trace of the matrix is closely related to the determinant, we search for users that yield the largest determinant of their channel auto-correlation matrix. The proposed technique utilizes the determinant row-exchange criterion (DREC) for computing the determinant-changing ratio, which is generated whenever a user is replaced by one of a group of pre-selected users. Based on the ratio computed by the DREC, the combination of users providing the largest changing ratio is selected. In order to identify the optimal combination, the DREC procedure is repeated until user replacement provides no increase in the determinant. Through computer simulations of four transmit antennas, we show that the bit error rate (BER) per signal-to-noise ratio (SNR) as well as the sum-rate performance provided by the proposed method is comparable to that of the full search method. Furthermore, using the proposed method, a partial replacement of users can be performed easily with a new user who provides the largest determinant.