Recently, a new technique for investigating the zero-field, eight-vertex model on the square lattice using corner transfer matrices was suggested by Baxter. In this paper these ideas are applied to the anisotropic, ferromagnetic, triangular Ising lattice in zero field below its critical temperature. The diagonal form of the corner transfer matrix for the triangular lattice shows essentially the same structure as that for the square Ising lattice. The spontaneous magnetization can be obtained easily and agrees with that previously derived.