A coupled cell system is a network of dynamical systems, or 'cells', each of which is given by ODEs. The network architecture is a directed graph and it represents interactions between the dynamical systems on cells. The main motivation of the study of coupled cell system, formulated by M. Golubitsky, I. Stewart et al., is to understand dynamics of the whole system from its network architecture. As the number of cells in the network grows the coupled cell system would be more and more complicated to analyse. To meet such difficulty, we develop an idea of getting at least partial information of the system from its subnetwork architecture. We show that for a certain type of network and a generic coupled cell system associated with that network, there exists a local invariant manifold given in a neighborhood of equilibrium, on which the coupled cell system behaves identically the same as a coupled cell system associated with a subnetwork of the original network.