We present the fourth edition of the Sloan Digital Sky Survey (SDSS) Quasar Catalog. The catalog contains 77,429 objects; this is an increase of over 30,000 entries since the previous edition. The catalog consists of the objects in the SDSS Fifth Data Release that have luminosities larger than M_i = -22.0 (in a cosmology with H_0 = 70 km/s/Mpc, Omega_M = 0.3, and Omega_Lambda = 0.7) have at least one emission line with FWHM larger than 1000 km/s, or have interesting/complex absorption features, are fainter than i=15.0, and have highly reliable redshifts. The area covered by the catalog is 5740 sq. deg. The quasar redshifts range from 0.08 to 5.41, with a median value of 1.48; the catalog includes 891 quasars at redshifts greater than four, of which 36 are at redshifts greater than five. Approximately half of the catalog quasars have i < 19; nearly all have i < 21. For each object the catalog presents positions accurate to better than 0.2 arcsec. rms per coordinate, five-band (ugriz) CCD-based photometry with typical accuracy of 0.03 mag, and information on the morphology and selection method. The catalog also contains basic radio, near-infrared, and X-ray emission properties of the quasars, when available, from other large-area surveys. The calibrated digital spectra cover the wavelength region 3800--9200A at a spectral resolution of ~2000. The spectra can be retrieved from the public database using the information provided in the catalog. The average SDSS colors of quasars as a function of redshift, derived from the catalog entries, are presented in tabular form. Approximately 96% of the objects in the catalog were discovered by the SDSS.
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