We report on a simplified representation of Multi-Input Multi-Output (MIMO) systems and propose a Minimum Bit Error Rate (MBER) diagonal precoder. Assuming that channel information can be available at the transmitter, we show that the proposed representation decouples the MIMO channel into parallel subchannels, which greatly facilitates and speeds up further processing. Using traditional criteria such as the minimum mean square error (MMSE) and the maximum capacity, eigen diagonal precoders and decoders can be obtained, leading to the same transmit and receive filters as those reported in the literature but in a simpler and faster way. A new diagonal precoder is also derived using the minimum bit error rate (MBER) criterion and compared to the others in term of bit error rate and achieved capacity. An approximation of the MBER precoder (AMBER) is finally proposed, whose performances remain close to the optimal in spite of its low complexity.