The woman, 62, contacted police after noticing what appeared to be a fraudulent transaction on the other side of the country.

When police started investigating, they say they found similar unauthorised transactions.

Inspector Gerard Powell said investigations into the fraud are ongoing as police look at transactions from other states as well.

He said the victim met and was befriended by the man on an online dating service midway through 2019.

He said the victim and the man communicated over a period of months and, during this time, the man arranged, through the woman, to use her bank account.

"Once he's accessed the account, he has continued to transfer money from her account at different times," Inspector Powell said.

The victim told police she had never met the man face to face despite giving him access to the account.

Inspector Powell said the investigation, while in its infancy, is ongoing.

"The matter initially reported to us as a fraudulent act which came to light in Western Australia," he said.

"After police began looking at the account, they have found a number of other fraudulent transactions linked to the account."

Inspector Powell said the incident served as a warning to others never to disclose their personal banking information to others.