RBS has revealed that nearly three out of every four of its customers who fall victim to a scam do not get any money back.
Figures from the RBS Group have revealed that from January to September this year almost 5,000 of the bank's customers fell victim to various scams - at a total cost of more than £25m.
The Edinburgh-based bank has reported that the average cost of falling for a scam has gone up by 40% since 2014, to more than £13,000.
The taxpayer-owned bank says the rate at which people are falling victim to frauds is on the increase with 900 cases reported in the third week of October alone - compared with 739 for the whole of September.
Terry Lawson, head of fraud at RBS told the BBC: "These figures show that the threat of scams is growing.
"The means by which fraudsters trick individuals into parting with their money is becoming more sophisticated, but it always ultimately depends on the individual transferring money out of their account.
"We would never contact a customer asking them to transfer money. If a customer of any bank is contacted by someone asking them to do this they should simply end the conversation and report the matter to the police."
The details emerged as communications firm TalkTalk was targeted in a cyber attack a week ago, in which it said bank account numbers and sort codes, like those printed on a cheque, may have been accessed.
A report by HP Enterprise Security suggest that cybercrime costs UK firms an average of £4.1 million a year.
The study found that the average cost of cyber-crime in the UK has steadily increased over the last three years.
In the fiscal year of 2013, costs totalled £3.07m, this rose to £3.86m in 2014, and this year the total again jumped to £4.12m.
A report by anti-virus and web security experts Symantec released in April said there were almost one million new cyber threats released online every day last year, with five out of six large companies globally targeted.
Estimates earlier this year suggest that up to £650million - has been stolen in approximately two years from financial institutions worldwide.
The fraud was detected by cyber security firm Kaspersky Lab.
The responsibility for the robbery rests with a multinational gang of cyber criminals, largely from Russia, Ukraine and other parts of Europe, as well as China.
The cyber criminals began by gaining entry into an employee's computer through 'spear phishing', infecting the victim with malware called Carbanak.
Criminals send authentic-looking emails that unsuspecting recipients clicked on, inadvertently infecting the bank's machines with the Carbanak malware.
They were then able to jump into the internal network and track down administrators' computers for video surveillance.
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