RateCity analysis showed the Big Four banks had hiked rates on their bonus saver accounts for one month but not the other.
CBA passed on the June rate hike of 0.50 per cent to its GoalSaver account, but did not pass on the May hike.
Westpac, NAB and ANZ, by contrast, have only passed on May’s 0.25-per-cent increase for their comparable products.
That’s despite all four major banks committing to passing on the rate hikes in full to their variable-rate-mortgage customers.
The big banks have been offering competitive home loan deals to attract new customers.
ANZ cut its lowest variable rate for new customers, and Westpac reintroduced a honeymoon rate that gives a bigger discount for two years.
The millions of savers who have got nothing extra from their bank this month have every right to be angry,” RateCity research director Sally Tindall said.
“It’s bitterly disappointing to see three of the Big Four banks haven’t yet moved savings rates an inch, when the cash rate has gone up by half of a per cent.
“With the cost of living rapidly rising, getting a decent rate on your savings account is becoming increasingly important.”
Tindall said 23 banks had hiked at least one savings account this month, including CBA, ING and Macquarie.
She said savers looking for a decent interest rate should compare their account to others in the market.
ING is offering the highest rate on a bonus saver account - 2.10 per cent through its Savings Maximiser account.
The BOQ Smart Saver Account and the Virgin Money Boost Saver are also offering competitive rates of 2.00 per cent.