Wada's representation is of Burau type

We consider the Magnus representation of the image of the braid group under a representation discovered by Wada. We first investigate the question about the reducibility of this representation and show that it is of Burau type. Next, we show that the images of the generators of the braid group under that representation are unitary relative to a hermitian matrix. This is similar to the well known result by Squier that asserts that the Burau representation of the braid group is unitary.