A minimum bit error rate (MBER) multiuscr detector (MUD) is considered for Direct-Sequence Code-Division Multiple-Access (DS-CDMA) communication systems with time-varying and frequency-selective fading channels. The BER cost function of the proposed MBER MUD is highly non-linear and may have several local minimum. It is shown that with some appropriate constraints the BER cost function of the MBER MUD is equivalent to a constrained optimization problem which has a unique global minimum in the feasible region. An efficient Newton method with a barrier parameter is developed for finding the coefficients of the proposed MBER MUD. The BER performance of the MBER MUD is compared to decorrelating (DEC) detector, linear minimum mean-square error (LMMSE) detector, and the maximum likelihood detector for time varying and Rayleigh distributed frequency-selective fading DS-CDMA channels. Monte-Carlo simulations show that the BER of the MBER MUD can be significantly lower than that of the DEC and the LMMSE multiuser detectors.