Last week, Clydesdale was fined £8.9 million by the Financial Conduct Authority after it forced 22,000 customers into higher mortgage repayments in order to rectify a previous error by bank staff.
The regulator said Clydesdale had failed to clearly spell out customers' rights following the bank's miscalculation on the repayments on more than 42,500 mortgages.
Clydesdale agreed to compensate those who were adversely affected, resulting in a total cost to the bank of about £42 million.
But it has now emerged that some customers who had already won redress years ago have received letters to say they are being paid compensation again.
One Twitter user who said they had received a double payment complained: "They can't even correct their errors properly...
"Now I've got the hassle of contacting them and trying to explain to them that I can't take their money as I already got it 3 years ago!"
He said: "We have agreed with the FCA that where any compensation has been paid previously this is deducted from the amount being credited to the mortgage.
"There are a small number of cases where previous complaints may not have been taken into account and we're contacting these customers to apologise for any inconvenience and to confirm the exact standing of their account."
Clydesdale, which is owned by National Australia Bank, sent letters to customers in 2009 which suggested that they had no alternative but to bring their mortgage repayments up to date.
But many customers could have rejected demands to repay the shortfalls caused by Clydesdale's calculation errors.
In total, the earlier blunder meant a £21.2 million shortfall in Clydesdale mortgages, with customers who underpaid left with outstanding mortgage balances higher than they should have been. The shortfalls range from less than £20 to more than £18,000, with an average of £970.