TSB was forced to apologise for another glitch - after it emerged that former customers found their direct debits had been cancelled and firms were apparently told that they had died.
Consumer help website MoneySavingExpert.com said it has heard from several former TSB customers who had switched away from the bank following its IT meltdown.
They reported receiving letters from various organisations offering their condolences.
The letters also say that their direct debits have been cancelled.
MoneySavingExpert said customers have then contacted those who have sent them the letters - and been told that TSB has said they have died.
A TSB spokeswoman said: "We are aware there was an issue with a small number of our customers switching from or closing their account with TSB, which resulted in an error in the cancellation or transfer of some of their direct debits.
"We are deeply sorry for any distress caused. We are working to rectify this issue and we are really sorry for the inconvenience caused."
MoneySavingExpert.com quoted a man from Merseyside who had switched away from TSB who said: "I have just had a letter from my council today saying that my house has now got a new owner/occupier. I rang them and they said that TSB had told them that I was deceased."
Another man who had switched from TSB to another bank told MoneySavingExpert he had four organisations, including his gas and electricity provider, contact his household and tell him that his direct debit had been cancelled because of his death.
He said: "I've had to phone every company and tell them I'm not dead and give them my new bank details, which I feel I shouldn't have to do, and they are all saying it's what TSB had told them."
Up to 1.9 million people using TSB's digital and mobile banking found themselves locked out of their bank accounts following an IT migration in April.
The bank's chief executive Paul Pester later told MPs on the Treasury Committee that 40,000 complaints had been received over a 10-day period - and promised they would be put right.