A path-oriented routing strategy is proposed for packet switching networks with end-to-end internal protocols. It allows switch pairs to communicate over multiple paths (for better network throughput), while maintaining knowledge of user connections at the network's endpoints only. The most significant aspect of this strategy lies in its flow assignment method. A distributed loop-free shortest path algorithm assigns a number to a path at the time it is created and this number remains valid through shortest path changes. Consequently, existing traffic can be maintained on existing paths, while new traffic is assigned to the current shortest paths. Stable multiple path routing is thus achieved without packet disordering. Abnormal conditions such as trunk failure and recovery and trunk congestion are dealt with by tagging routing updates with update causes. Simulation of this routing strategy shows that maximum network throughput (under a certain congestion constraint) can be increased substantially compared to a single path routing strategy.