Stabilization by decentralized control is an important problem in large scale systems and there has been an increasing interest in this area. The objective of this paper is to obtain the sufficient condition for an interconnected system to be stabilited by local feedback. Recently there has been many papers about this, and we further broaden the class of interconnections for which we can find a decentralized control to stabilize the overall system. The interconnection matrix may take any arbitrary time invariant values and this implies connective stability in some sense. The assumed model is mire general than most of previous ones, and as a special case, when each subsystem is given by companion form of a single inputs the result is compared with that of Ikeda and Siljak. The obtained result is illustrated by examples.