The Molonglo Southern 4 Jy Sample (MS4). I. Definition

We have defined a complete sample of 228 southern radio sources at 408 MHz with integrated flux densities S₄₀₈ > 4.0 Jy, Galactic latitude |b| > 10°, and declination -85° < δ < -30°. 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'', 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 S₁₇₈ > 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.