The strong gamma(k)-gamma H-cl(infinity) stabilization problem is addressed in this paper. Based on the bounded real lemma, an improved sufficient condition on strong H-infinity stabilization as well as its dual form is derived, which extends the ARE constraint in the former results into an inequality constraint. Two path-following algorithms are proposed to solve the associated optimization problems with BMI constraints, which lead to full order controllers. A numerical example is presented to demonstrate the effectiveness of the result.