In the construction of an X-ray-selected sample of galaxy clusters for cosmological studies, the authors have assembled a sample of 495 X-ray sources which were found to show extended X-ray emission in the first processing of the ROSAT All-Sky Survey (RASS I), the Northern ROSAT All-Sky (NORAS) Galaxy Cluster Survey Catalog. The sample covers the celestial region with declination >=0 degrees and Galactic latitude |b| >= 20 degrees, and comprises sources with a Position Sensitive Proportional Counter (PSPC) count rate >= 0.06 counts/s and a source extent likelihood of L >= 7. In an optical follow-up identification program, the authors found 378 (76%) of these sources to be clusters of galaxies. It was necessary to reanalyze the sources in this sample with a new X-ray source characterization technique to provide more precise values for the X-ray flux and source extent than obtained from the standard processing. This new method, termed growth curve analysis (GCA), has the advantage over previous methods in its ability to be robust, to be easy to model and to integrate into simulations, to provide diagnostic plots for visual inspection, and to make extensive use of the X-ray data. The source parameters obtained assist the source identification and provide more precise X-ray fluxes. This reanalysis is based on data from the more recent second processing of the ROSAT Survey, RASS II. The authors present a catalog of the cluster sources with the X-ray properties obtained as well as a list of the previously flagged extended sources that are found to have a non-cluster counterpart. In their paper, they discuss the process of source identification from the combination of optical and X-ray data. To investigate the overall completeness of the cluster sample as a function of the X-ray flux limit, they extended the search for X-ray cluster sources to the RASS II data for the northern sky region between 9 and 14 hours in right ascension. They included the search for X-ray emission from known galaxy clusters as well as a new investigation of extended X-ray sources. In the course of this search, they found X-ray emission from 85 additional Abell clusters and 56 very probable cluster candidates among the newly found extended sources. A comparison of the X-ray cluster number counts of the NORAS sample with the ROSAT-ESO Flux-limited X-ray (REFLEX) Cluster Survey results leads to an estimate of the completeness of the NORAS sample of ROSAT All-Sky Survey (RASS) I extended clusters of about 50% at an X-ray flux of FX(0.1-2.4 keV) = 3 x 10-12 ergs s^-1 cm^-2. The estimated completeness achieved by adding the supplementary sample in the study area amounts to about 82% in comparison to REFLEX. The low completeness introduces an uncertainty in the use of the sample for cosmological statistical studies that will be cured with the completion of the continuing Northern ROSAT All-Sky (NORAS) Cluster Survey project. This table was created by the HEASARC in June 2005 based on CDS table J/ApJS/129/435, table1.dat through table9.dat inclusive. This is a service provided by NASA HEASARC .