This is a catalog of 203 clusters of galaxies serendipitously detected in 647 ROSAT PSPC high Galactic latitude pointings covering 158 square degrees. This is one of the largest X-ray-selected cluster samples, comparable in size only to the ROSAT All-Sky Survey sample of nearby clusters (Ebeling et al. 1997). Clusters in the inner 17.'5 of the ROSAT PSPC field of view are detected using the spatial extent of their X-ray emission. Fluxes of detected clusters range from 1.6 x 10^-14 to 8 x 10^-12 ergs s^-1 cm^-2 in the 0.5-2 keV energy band. X-ray luminosities range from 10^42 ergs s^-1, corresponding to very poor groups, to ~5 x 10^44 ergs s^-1, corresponding to rich clusters. The cluster redshifts range from z = 0.015 to z > 0.5. The catalog lists X-ray fluxes, core radii, and spectroscopic redshifts for 73 clusters and photometric redshifts for the remainder. Of 223 X-ray sources, 203 have been optically confirmed as clusters of galaxies. Of the remaining 20 sources, 19 are likely false detections arising from blends of unresolved point X-ray sources. Optical identifications of the remaining object are hampered by a nearby bright star. Above a flux of 2 x 10^-13 ergs s^-1 cm^-2, 98% of extended X-ray sources are optically confirmed clusters. The number of false detections and their flux distribution are in perfect agreement with simulations. The log N-log S relation for clusters derived from this catalog shows excellent agreement with counts of bright clusters derived from the Einstein Extended Medium Sensitivity Survey and the ROSAT All-Sky Survey. At fainter fluxes, its log N-log S relation agrees with the smaller area WARPS survey. The cluster counts appear to be systematically higher than those from a 50 square degree survey by Rosati et al. This database was created by the HEASARC in December 2001 based on the CDS/ADC catalog J/ApJ/502/558/ (table3.dat). This is a service provided by NASA HEASARC .