Most high-end switches use an input-queued or a combined input- and output-queued architecture. The switch fabrics of these architectures commonly use an iterative scheduling system such as iSLIP. Iterative schedulers are not very scalable and can be slow. We propose and study a new fabric scheduling scheme that is fast and scalable. This scheduler finds maximum matching in a single iteration. It provides full throughput and incurs very low delay. It is fair and of low complexity. It greatly outperforms traditional iterative schedulers. It also renders arbitration egress memory unnecessary. Its only drawback is that it requires the support of several reads to an input memory at the same time. But simulations show this drawback is immaterial as read multiplicity is very low in various traffic conditions.