Phase diagram is determined for the spin-1 Ising system described by the Hamiltonian æ = HΣ(subscript i)si + ΔΣ(subscript i)si^2 - JΣ(subscript <ij>)(si^2)(sj^2). The determination is exact for ferromagnetic interactions (J>0) and schematic for antiferromagnetic interactions (J<0).