In this note, the static output feedback stabilization problem is addressed using the linear matrix inequality technique. A necessary and sufficient condition for static output feedback stabilizability for linear time-invariant systems is derived in the form of a matrix inequality. The extension of the result to H-infinity control is studied. An iterative LMI (ILMI) algorithm is proposed to compute the feedback gain. Numerical examples are employed to demonstrate the effectiveness and the convergence of the algorithm.