A state-space-based design method is developed to construct strongly stabilizing controllers for a class of MIMO plants. The problem is reduced to solving an algebraic Riccati equation (ARE) which appears in the solution of a two-block H-infinity problem. Strongly stabilizing controllers designed here are of the same order as the plant. Two sets of finite-dimensional strongly stabilizing controllers are parameterized in terms of linear fractional transformations. Further optimization guidelines are given to find stable H-infinity controllers from these parameterizations. Stability robustness margins, with respect to coprime factor uncertainties,are determined for the controllers designed from the proposed method.