A new linear multiuser detector that directly minimizes the bit-error rate (BER) subject to a set of reasonable constraints is proposed. It is shown that the constrained BER cost function has a unique global minimum. This allows us to develop an efficient Newton barrier method for finding the coefficients of the proposed detector using information about timing, amplitudes, channels, and the signature signals of all users. Although the new detector cannot be shown to be optimal among linear multiuser detectors without the constraints imposed, extensive simulations demonstrate that it achieves the lowest BER. Furthermore, in some cases, the BER of the proposed detector can be significantly lower than that of the decorrelating and MMSE detectors.