This paper considers the synthesis of a static output feedback H-infinity controller for linear discrete-time systems subject to polytopic uncertainties and external disturbances. Based on the selection of parameter-dependent Lyapunov function and the use of a bounding matrix inequality followed by a congruent transformation, a set of sufficient bilinear matrix inequality conditions is obtained. Employing the well known cone complementarity technique, the nonconvex optimization problem is converted into a convex minimization one formulated with linear matrix inequality (LMI) conditions. Several numerical examples are presented to show that the proposed method yields less conservative disturbance attenuation rates than those reported in the literature.