Network-based parallel processing using commodity personal computers has been widely developed. Since such systems require high degree of flexibility and scalability of wiring, a high-speed network with an irregular topology is often needed. In traditional routing algorithms for irregular networks, available paths are considerably restricted in order to avoid deadlocks. In this paper we propose a novel routing algorithm called left-up-first turn routing (L-turn routing), which makes a better traffic balancing in irregular networks by building a specific spanning tree. Result of simulations shows that L-turn routing achieves better performance than traditional ones with each topology.