A closed-form expression to determine an average error rate for synchronous DS-CDMA multi-user detector is derived based on the transformation matrix (TM) algorithm proposed in . The derived expression for average bit error rate (BER) can be used to produce higher and consistent values of signal-to-noise ratio (SNR) that consequently results good quality signal. In addition, the closed-form expression can be used to quantify the multiple access interference (MAI) for a desirable BER performance by which unwanted signals or interference can be suppressed relative to the desired signal at the receiving end. The derived closed-form expression for BER is not only shown to substantially improve the performance of the multiuser detectors by means of higher values of SNR but also has much lower MAI. The performance measure adopted in this paper is the achievable bit rate for a fixed probability of bit error (10 -7) and the consistent values of SNR.