A generalised vector precoding (VP) design based on the minimum bit error rate (MBER) criterion is proposed for multiuser transmission in the downlink of a multiuser system where the base station (BS) equipped with multiple transmit antennas communicates with single-receive-antenna mobile station (MS) receivers each having a modulo detection device. Our transmit preprocessing scheme generates the effective symbol vector based on the MBER criterion, given the knowledge of the channel state information and the current information symbol vector to be transmitted. The proposed MBER based generalised VP algorithm is shown to outperform even the powerful minimum mean-square-error VP benchmark, particularly for rankdeficient systems where the number of BS's transmit antennas is smaller than the number MSs supported.