An analysis of a quaternary direct-sequence spread-spectrum multiple-access communication system is presented. The system uses a correlation receiver and random signature sequences in an additive white Gaussian noise channel. The multiple-access interference (MAI) is analysed using a product of symmetric multinomials. The analysis is greatly simplified by assuming independent MA1 for different interferers. The result is a procedure for the determination of independent MA1 probability density functions (pdf). The pdf's are subsequently used to obtain an approximation to the probability of bit error.