A higher-order statistics based minimal transmit redundancy space-time FIR precoder-blind equalizer is proposed. For most block based transmission systems such as OFDM, a long guard period, which is longer than or equal to the channel order, is required to avoid inter-block interference. This guard period is a type of redundancy which consumes valuable bandwidth. The blind equalizer that we have proposed can blindly equalize the received precoded signal without the long guard period requirement. Simulation results have shown that the BER performance gain increases as more received data are used to design the equalizer which allows accurate estimation of the cumulant matrices. The proposed algorithm was also shown to be robust toward channel order overestimation.