The catalog contains 1595 photoelectric radial-velocity observations for 790 bright southern stars of spectral type F5 and later. One of the purposes of this project is to make a complete southern sky radial velocity coverage using the second CORAVEL photoelectric radial velocity scanner. The first CORAVEL operating at Observatoire de Haute-Provence was used to observe the stars in the Northern Hemisphere. Two CORAVEL observations per star were made with CORAVEL photoelectric radial velocity scanner on the Danish 1.54-m telescope at ESO, La Silla, Chile. The mean velocities are accurate to about 0.15 km/s r.m.s. for sharp-lined constant stars, errors increasing somewhat for stars with significant rotation. The present data complete and supersede the preliminary data for 500 stars supplied in advance of publications for inclusions in the fourth edition of The Bright Star Catalogue. At the time this project was planned, there were still some 1500 stars in The Bright Star Catalogue for which no radial-velocity information was available -- virtually all of them in the Southern Hemisphere. For the stars of type F5 and later, photoelectric scanning techniques can be used with much increased efficiency and accuracy. The catalog includes HD numbers with component designation for visual binary components from Jeffers et al. (1963), HR numbers, FK4 or FK4 Supplement numbers, visual magnitudes, MK spectral classes, mean velocities, velocity variability parameters, rotation classes as assigned from the measured linewidths, and remarks and information for individual measurements in a separate file.