Synchronization of a complex network with switched coupling is considered. In particular, we establish a simple method to obtain a proper coupling strength for the network. Via switched system theory, with this coupling strength, we achieve synchronization of the network without requiring synchronizability of all possible configurations. First, we convert the network into a switched system with the reduced number of subsystems which are static complex networks whose configurations are non isomorphic via partitioning all possible configurations generated from the switched coupling. Then, we obtain a finite number of coupling strength candidates from the subsystems. By applying the average dwell time approach, synchronization of the network is indeed achieved with the coupling strength chosen among the candidates.