Incorrect internet payment, refuse to reverse

By mistake I paid r4000 into the wrong persons account. FNB refuses that the internet payment gets reversed. Its my money, not theirs and not the account holder. I phoned immediately after doing the transfer and completed the forms to ask for a reversal. Its *****ing, u keeping money that don't belong to you. There should be a process by which you can reverse a payment if you made a mistake.