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Next generation switches/routers will have to use switching fabrics in order to achieve the desired capacity and speed to support growing Internet traffic. For high-performance switches and routers the Clos switching fabric is very attractive because of its modular architecture and scalability. A great many packet dispatching schemes for three-stage buffered and bufferless Clos switching fabrics were proposed in the literature. Some of them provide high throughput under uniform, others under nonuniform traffic distribution. In this paper the modified MSM Clos switching fabric and a very simple packet dispatching scheme, called Static Dispatching with Rapid Unload of Buffers (SDRUB), are proposed. We show via simulation that this modified switching fabric and the described scheduling deliver very good performance in terms of throughput, cell delay and input buffers size under different traffic distribution patterns.