The WK-recursive network well conforms to implementation of large distributed systems due to its many favorable properties. In this paper, we employ the concept S₃ group to establish an efficient look-ahead routing algorithm for the triplet-based WK-recursive network. Remarkably, we introduce a data flow model to categorize message traffic as six flow models. For the sake of simplicity, we further leverage the permutation group S₃ to transform different flow models to one model and hence routing computing can be performed in the same model. It is demonstrated that our proposed design can achieve better network performance.