At 07:00 (AEST), the Australian dollar was buying 61.73 U.S. cents, up from 60.88 U.S. cents on Tuesday.
On Tuesday the RBA kept the official interest rate at 0.25 percent after lowering it at an emergency meeting in mid-March.
"The RBA kept policy on hold as expected at 0.25 percent for both cash rate and 3 year bond but its statement leant to the positive side and included a suggestion that it would probably reduce the pace of bond purchases," Westpac Bank economists said in a morning note.
"AUD/USD retained most of its post-RBA gains, steadying around 61.70 U.S. cents."
At 09:30 (AEST), the local unit was buying 61.73 U.S. cents.
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