Because of the high computational complexity of the optimal multiuser detector, many suboptimal multiuser detectors have been proposed for rejecting multiple access interference. Parallel interference cancellation (PIC) are among the most promising receivers for future CDMA systems. Because of complexity of analysis of PIC systems, most work has relied heavily on simulation techniques to supplement analysis. This paper considers a simple model for hard-decision multistage parallel interference cancellation within a code-division multiple-access(CDMA) system. By analyzing the structure and statistical characteristics of residual multiple access interference at stage 2 of the parallel interference cancellation algorithm, we present an analytical expression for the probability of bit error, using both Gaussian approximation (GA) and improved Gaussian approximation (IGA) for residual MAI, Calculation results are compared with simulation results, The BER at any stages of interference cancellation can also be recursively computed using this method.