At the close of trade, the S&P/ASX 200 ended down 29 points, or 0.5 per cent, to 5378.6, while the All Ordinaries fell 0.5 per cent, or 26 points, to 5447.8, sinking in the afternoon despite two valiant attempts to claw back above 5400 points.

But the month was good to the index, finishing up 2.4 per cent, the best month of May since 2005. Morgans private client adviser Steve Greentree said the unseasonably strong performance for May was spurred by the weak inflation numbers and the interest rate cut early in the month.

"The lower than expected inflation numbers and the prospect for more rate cuts saw investors move into the high yielding sectors of the market," he said.

He also suspected short-covering for those investors hoping to capitalise on the "sell in May and go away" adage.

"After the first pretty dreadful months this year, people would have thought, statistically speaking, this time of the year is usually weak. I think people have been caught short," Mr Greentree said.

Tuesday's weak session bucked a positive day around the region in the absence of a lead from London and New York, both closed for public holidays. China's sharemarkets posted a three-week high, rallying around 3 per cent in late Tuesday trade, while Hong Kong and Japanese equities were 1.6 per cent and 1 per cent higher, respectively.

Meanwhile surprising local data pushed the Australian dollar more than half a penny higher to US72.43¢ after surprisingly strong net exports data sent economists scrambling to revise their first quarter GDP forecasts. First quarter net exports will add 1.1 per cent to economic growth over the period, according to data from the Australian Bureau of Statistics, much stronger than the expected 0.7 per cent.

Economists now expect ABS figures released Wednesday morning will show the Australian economy grew by 0.8 per cent over the March quarter, from a prior median estimate of 0.6 per cent, according to Bloomberg. The estimate for annual GDP growth was upped to 2.8 per cent from 2.6 per cent.

Tuesday's data also added weight to the consensus opinion that the Reserve Bank of Australia will keep rates steady at 1.75 per cent at its meeting next week.

The banks, beneficiaries of May's rate cut, were among biggest drags on the index on Tuesday. Commonwealth Bank of Australia fell 1 per cent to $77.43, Westpac Banking Corporation lost 0.3 per cent to $30.78, ANZ Banking Group fell 0.8 per cent to $25.48 and National Australia Bank fell 0.3 per cent to $27.18.

In the miners, BHP Billiton fell 0.8 per cent to $19.08 while Rio Tinto ended 0.2 per cent lower to $44.69.

Lifting the index was Newcrest Mining, recovering the previous day's losses, adding 1.3 per cent to $19.07, and Aristocrat Leisure, one of the best performers in recent months, up 0.9 per cent to $12.86. Industrials also fared well, and Transurban added 0.7 per cent to $74.87, while Incitec Pivot rose 2.1 per cent to $3.45.

Among the other blue chips, Telstra sunk 1.4 per cent to $5.59, Wesfarmers shrunk 2.1 per cent to $40.63, and Woolworths lost 1.2 per cent to $22.12, both paring Monday's gains.

The best performing stock for the day was Select Harvests, the almond farmer continuing its strong recovery, up 6.7 per cent to $7.15 a day after boosting its production volume forecast for 2016. The lagger was Flexigroup, falling 6.8 per cent to $2.06 and to four year lows after it flagged its 2016 and 2017 financial year profits would be weaker than expected.

Information technology and consumer discretionary were the only sectors in the black, up 0.1 per cent each. Energy fell the most, down 1.5 per cent.