The relationship between El Niño-Southern Oscillation (ENSO) indices and precipitation (P) in some parts of Australia has previously been shown to be non-linear on annual and seasonal time scales. Here we examine the relationship between P and the Southern Oscillation Index (SOI) at all Australian locations and in all seasons. We show that in many Australian regions, there is more-than-expected P during strong La Niña years (SOI>13), but less-than-expected drying during strong El Niño years (SOI<-13). Statistically significant non-linearities are found over northern NT, QLD and parts of WA during SON, and parts of QLD, NSW, and VIC during DJF, when regressing P against June-December SOI. During the MAM immediately preceding a June-December ENSO year, and during JJA, the rainfall-SOI relationship is linear over most of the country. Systematic eastward shifts in P patterns can explain non-linearities over northern Australia, but do not explain non-linearities southward of approximately 20˚S. The seasonal P distribution is decomposed into FP, the fraction of days on which P falls, and PD, the amount of rain per day on days when P is non-zero. Both FP and PD display a non-linear relationship with SOI similar to the P-SOI relationship, although the relative influence of each term on P is spatially and seasonally dependent.