This paper addresses the problem of nonlinear decentralized state feedback stabilization for a class of large-scale systems with strong interconnections. The interconnections and their bounds are general functions of all the states. By developing a new recursive design method, a decentralized state feedback controller is successfully constructed for the large-scale system. The novelty of the proposed method is that a Lyapunov function in an appropriate product integral form is introduced at each step so that the recursive design can be carried out. A numerical example is given to illustrate the effectiveness of the proposed method. (C) 2014 Elsevier Ltd. All rights reserved.