Existing methods for routing of interconnection networks are optimized for a small group of well defined topologies. Currently, system owners and system integrators are looking for ways to connect two or more existing topologies into one, and thereby create a unified system out of several subsystems. Such integration of multiple networks is supported through e.g. The subnet routing functionality i InfiniBand. In this paper we show that the routing problem of such integration is unsolved, because the integration of two deadlockfree subsystems may lead to routing deadlock. Thereafter we present a theory and a methodology for combining multiple networks in a deadlock-free manner. Through experiments we show that the methodology is able to connect different classes of pre-defined topologies with a definable number of interconnecting links. We demonstrate that we are able to maintain the original routing strategy in the sub-networks, and still get close to full utilization of the bridging links. Finally we show that the methodology is computationally feasible.