This note presents two coupled Lyapunov-like conditions under which a linear discrete-time system can be stabilized by static output feedback. The originality of these conditions is their relation tothe well-known coupled Sylvester equations that describe both the (A,B) and (C,A)-invariance of a subspace. For systems verifying Kimura’s condition, we show that output feedback stabilizing gain matrices can be computed through the successive resolution of two standard convex programming problems. Numerical results are provided to show the effectiveness of the proposed approach.