ANZ's composite job advertisements indicator fell 1.3 per cent last month.
But as that followed five months of solid increases, the bank's economists still expect the unemployment rate to fall over coming months.
The indicator reflects jobs ads in newspapers and online, and historically has a tight fit to the official unemployment rate six months later.
The unemployment rate is 6.5 per cent and has oscillated around that level for the past two years.
Last month saw a 3.9 per cent drop in jobs advertised in newspapers, offset by a 2.2 per cent rise in internet listings.
Another labour market indicator ANZ uses combines the composite jobs ads series, the number of people drawing the unemployment benefit, and hiring intentions and other indicators from the National Bank's monthly survey of business sentiment.
ANZ economist Sharon Zollner said that index was pointing to a gradually falling unemployment rate.