This note treats the problem of stabilization of linear systems by static output feedback using the concept of (C, A, B)-invariant subspaces. The work provides a new characterization of output stabitizable (C, A, B)-invariant subspaces through two coupled quadratic stabilization conditions. An equivalence is shown between the existence of a solution to this set of conditions and the possibility to stabilize the system by, static output feedback. An algorithm is provided and numerical examples are reported to illustrate the approach.