To keep flat brick stitch beadwork from tapering, you need to perform an increase at the start of each row. The diagram above shows the thread path for making these increases. Notice that although you pick up two beads to begin each row (as always), you pass your needle beneath the first bridge of thread in the previous row, rather than the second bridge of thread (which would result in a automatic decrease).
This technique results in rows with equal numbers of beads. The beadwork is even, although the rows remain offset by the space of one-half bead.
Be aware that in some brick stitch tutorials, the beadwork is kept even without any reference to making increases. In those cases, the increases are implied, and you should still make them.