Much data on the Galactic polarized radio emission has been gathered in the last five decades. All-sky surveys have been made, but only in narrow, widely spaced frequency bands, and the data are inadequate for the characterization of Faraday rotation, the main determinant of the appearance of the polarized radio sky at decimetre wavelengths. We describe a survey of the polarized radio emission from the Southern sky, aiming to characterize the magneto-ionic medium, particularly the strength and configuration of the magnetic field. This work is part of the Global Magneto-Ionic Medium Survey (GMIMS). We have designed and built a feed and receiver covering the band 300 to 900 MHz for the CSIRO Parkes 64-m Telescope. We have surveyed the entire sky between declinations -90 and +20 degrees. We present data covering 300 to 480 MHz with angular resolution 81 to 45. The survey intensity scale is absolutely calibrated, based on measurements of resistors at known temperatures and on an assumed flux density and spectral index for Taurus A. Data are presented as brightness temperatures. We have applied Rotation Measure Synthesis to the data to obtain a Faraday depth cube of resolution 5.9 radians per metre squared, sensitivity of 60 mK of polarized intensity, and angular resolution 1.35 degrees. The data presented in this paper are available at the Canadian Astronomy Data Centre.