  We present a catalog of 345,000 stars with proper motions \mu > 20 mas/yr and
magnitudes r' <20, drawn from the intersection of the SDSS Data Release One and
USNO-B. We first use SDSS quasars to correct the proper motions in each of the
two source catalogs, finding that these corrections for systematics are
comparable to the statistical errors. The combined proper motions have errors
of \sigma_\mu=4.0 mas/yr, significantly better than any previous catalog at
these magnitudes. While cross-correlating SDSS and USNO-B removes the vast
majority of the very large number of spurious proper-motion stars in each, some
contamination remains, especially at faint magnitudes, r' > 19.5, and high
proper motions. We present a diagrammatic method to estimate the level of
contamination in selected subsets of the catalog, which should be useful for
choosing appropriate selection criteria for various applications.
