We present the redshift data for a survey of galaxies selected from the data base of the Infrared Astronomical Satellite (IRAS). This survey extends the 1.936 Jy sample of Strauss et al. (1992) from a flux limit of 1.936 Jy at 60 microns to 1.2 Jy. The survey extension consists of 3920 sources in the flux interval 1.2 - 1.936 Jy of which 2663 are galaxies with measured redshifts. Fourteen objects (0.52%) do not have redshifts. The survey covers 87.6% of the sky. The data for the complete 1.2 Jy survey (the data presented here in addition to that of Strauss \etal 1992) may be obtained in a machine-readable form from the National Space Science Data Center and from the anonymous ftp site given above