A simple exact error rate analysis is presented for random binary direct sequence code division multiple access (DS-CDMA) considering a general pulse shape and flat Nakagami Fading channel. First of all, a simple model is developed for the multiple access interference (MAI). Based on this, a simple exact expression of the characteristic function (CF) of MAI is developed in a straight forward manner. Finally, an exact expression of error rate is obtained following, the CF method of error rate analysis. The exact error rate so obtained can be much easily evaluated as compared to the only reliable approximate error rate expression currently available, which is based on the Improved Gaussian Approximation (IGA).