The regular matroids mark an interesting half-way stage between the matroids corresponding to graphs on the one hand, and the binary matroids, that is matroids which are representable over GF(2), on the other. Perhaps the most famous result to date in all of matroid theory is Tutte's characterization of regular matroids by means of forbidden minors [2]. An interesting feature of regular matroids is their close relationship with an important class of matrices, the unimodular matrices [4] (note that the entries of a unimodular matrix are all $0$ or $\pm1$). Our aim in this paper is to give some algebraic properties of the standard representatives matrices of regular matroids.