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In this paper, a minimum bit-error rate (MBER) linear multi-user detection (MUD) algorithm for time-varying frequency-selective fading direct-sequence code-division multiple-access (DS-CDMA) channels is proposed. The BER cost function of the MUD is highly non-linear and may have several local minimum. It is shown that with some appropriate constraints the MBER MUD problem is equivalent to a constrained optimization problem and it has one global minimum in the feasible region. Proposed algorithm finds coefficients of the MUD and also employs Newton method for iterations and Golden-Section method for line search. The BER performance of the MBER MUD is compared to Decorrelating (DEC) and Linear Minimum Mean Square Error (LMMSE) MUD. As shown by Monte-Carlo simulations, in most cases, the BER performance of the MBER MUD is lower than that of decorrelating and LMMSE detectors.