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The scalability of Clos-network switches makes them an alternative to single-stages switches for implementing large-size packet switches. This paper introduces a cell dispatching scheme, called Maximum Weight Matching Dispatching (MWMD) scheme, for buffered Clos-network switches. The MWMD scheme is based on a maximum weight matching algorithm for input-buffered switches. This paper shows that, with request queues in the buffered Clos-network architecture, the MWMD scheme is able to achieve a 100% throughput for independent admissible traffic, without allocating any buffers in the second stage and without expanding the internal bandwidth. As a practical scheme, a maximal oldest-cell-first matching dispatching (MOMD) scheme is also introduced. MOMD shows that using a finite number of iterations in the dispatching scheme, the throughout under unbalanced traffic pattern can be high.