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The pair, who are not believed to be known to each other, were captured on CCTV carrying out the same crime in South Auckland less than a week apart.
In the first incident, a man withdrew a large amount of cash from a victim's bank account at an ANZ bank ATM on Hunters Corner, Papatoetoe on January 22, police said.
The eftpos card had been lost when its owner dropped his wallet on Great South Road earlier that day.
The second incident involved bank cards from an elderly man's stolen wallet.
Police said the wallet had been reported as stolen on January 20, and since then a woman has been captured on camera using bank cards from the wallet to withdraw cash in the Otara area.
"These offenders have shown that they have no issue using someone else's cards to get access to their money," Detective Malakai Tohi of the Counties Manukau police financial investigation group said.
"We'd like to apprehend them as soon as possible and we know that someone will recognise the people in the pictures."
HAVE YOUR BANK CARDS BEEN STOLEN?
* Arrange to have your cards cancelled by your bank - if possible go into your nearest branch, otherwise call the number provided on your bank's website
* Report the crime to police
* Do not give your PIN to anyone
* Do not write your PIN down with your bank cards
* Tell police if you receive any suspicious phone call asking for your PIN
* Your bank or the police will never ask you for your PIN
Anyone who recognises the people pictured should call Detective Malakai Tohi on 09 262 2662 or 021 191 6137. Information can be reported anonymously to the organisation Crimestoppers on 0800 555 111.