  We have defined a complete sample of 228 southern radio sources at 408 MHz
with integrated flux densities S_408 > 4.0 Jy, Galactic latitude |b| > 10 deg
and declination -85 deg < delta < -30 deg. The main finding survey used was the
Molonglo Reference Catalogue. We describe in detail how the Molonglo Southern 4
Jy sample (MS4) was assembled and its completeness assessed. Sources in the
sample were imaged at 843 MHz with the Molonglo Observatory Synthesis Telescope
to obtain positions accurate to about 1 arcsec, as well as flux densities and
angular sizes; follow-up radio and optical observations are presented in Paper
II. Radio spectra for the MS4 have been compiled from the literature and used
to estimate flux densities at 178 MHz. The strong-source subset of MS4, with
S_178 > 10.9 Jy (SMS4), provides a southern sample closely equivalent to the
well-studied northern 3CRR sample. Comparison of SMS4 with 3CRR shows a
reassuring similarity in source density and median flux density between the two
samples.
