This paper proposes a large scale broadband self-routing switching network based on the three-stage construction of sort-banyan switch modules. The proposed switching network uses only one kind of module, preserves the cell sequencing of a service, and is robust for all patterns of load on the ports. A multistage three-phase algorithm is designed to control the delivery of cells. The switching network is input queued and delivers at most one cell in a cell time to each output port from one of the input ports which request cell delivery to that output port. The maximum throughput of the switching network is shown to be 0.458 which is about 78% of that of a single-stage sort-banyan switching network. With a buffer size of 20 cells, we can achieve a 40 percent loading with almost no buffer overflow. Parallelism is easily achieved by having multiple switching planes. With 4 switching planes, we show that the network is close to being output-queued.