The CORNISH project is the highest resolution radio continuum survey of the Galactic plane to date. It is the 5 GHz radio continuum part of a series of multi-wavelength surveys that focus on the northern GLIMPSE region (10° < l < 65°), observed by the Spitzer satellite in the mid-infrared. Observations with the Very Large Array in B and BnA configurations have yielded a 1.''5 resolution Stokes I map with a root mean square noise level better than 0.4 mJy beam 1. Here we describe the data-processing methods and data characteristics, and present a new, uniform catalog of compact radio emission. This includes an implementation of automatic deconvolution that provides much more reliable imaging than standard CLEANing. A rigorous investigation of the noise characteristics and reliability of source detection has been carried out. We show that the survey is optimized to detect emission on size scales up to 14'' and for unresolved sources the catalog is more than 90% complete at a flux density of 3.9 mJy. We have detected 3062 sources above a 7σ detection limit and present their ensemble properties. The catalog is highly reliable away from regions containing poorly sampled extended emission, which comprise less than 2% of the survey area. Imaging problems have been mitigated by down-weighting the shortest spacings and potential artifacts flagged via a rigorous manual inspection with reference to the Spitzer infrared data. We present images of the most common source types found: H II regions, planetary nebulae, and radio galaxies. The CORNISH data and catalog are available online at http://cornish.leeds.ac.uk.