A new self-routing network constructed from the sorting and the routing cells is proposed. The complexity of the new network is roughly twice as much as that of a pure banyan network. The new network can be viewed as an implementation of the load-sharing network  which requires a very simple management. Its performance under uniform and nonuniform traffic models is analyzed for the unbuffered case. It is found that a higher degree of nonuniformity results in a better performance for certain form of nonuniform traffic matrices. Simulations are performed to obtain the normalized throughputs and mean packet delays for the single-buffered case. Different from single-buffered pure banyan networks , the mean delay of high-traffic packets is smaller than that of low-traffic packets for a particular form of nonuniform traffic matrices. In addition to performance improvement, the new network is easy to diagnose. Some variations of the proposed network are also studied.