A collaboration between the Space Telescope Science Institute (STScI) and the Astronomisches Rechen-Institut has produced an astrometric re-reduction of the Guide Star Catalog (GSC) published by Lasker et al. This version, GSC 1.2, has dramatically reduced the systematic errors present in the GSC 1.1. As shown by Taff et al., the positions in the GSC 1.1 are affected by plate-based systematic distortions that are largest at the plate edges (1.0" in the north and 1.2" in the south). In addition, Morrison et al. have shown that these positions also suffer from systematic errors which are a function of magnitude and radial distance from the plate center. This effect is small for radii under 2.7d from the plate center, then rapidly increases, producing an average offset of the faint stars (15 mag) versus the reference stars (10 mag) of 0.9" at the plate edges. Since the magnitude term was similar for the two main plate collections comprising the GSC, which were taken with different telescopes, exposure times, emulsions, and filters, we believe this effect is common to fast wide-field-of-view Schmidt plates. In this paper we report on the astrometric quality of the GSC 1.2 and present the method we developed (for large plate collections) to quantify and reduce the positional errors which are dependent on location on the plate and magnitude. Instruction for obtaining the catalog may be obtained from the STScI World Wide Web site, or the user can obtain the catalog directly from CDS (Centre de Donneés astronomiques de Strasbourg). This version of the catalog has not been installed in the HST Guide Star Selection system. Therefore this version must not be used for HST observation planning.