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We propose a bifurcated queueing approach to breaking the well-known 0.586 barrier for the throughput of input queued switches with head-of-line blocking. Each input line maintains a small number k of parallel queues, one for each of a set of k mutually exclusive subsets of the set of output-port addresses. We generalize the analysis of Karol et al. (1987) and show that the upper bound on throughput is (1+k)-/spl radic/1+k/sup 2/, k=1, 2, 3, .... We point out that even for k=2, there is a significant improvement in throughput and that as k increases, the throughput approaches one.