Nationwide will only offer 85% loans to new customers
The Nationwide Building Society has introduced a mortgage allowing borrowers to take loans worth 125% of the value of the home they are buying.
It will only be available to existing customers in negative equity who want to move house.
Negative equity means that the value of someone's home is less than the amount they owe on their mortgage.
Nationwide said the deal was a very "niche offer" and that not everyone in negative equity would qualify.
The Financial Services Authority is considering limiting mortgage loans to 100% of a property's value.
'No more risk'
The Nationwide only offers new customers mortgages worth 85% of the value of the home they want to buy.
NEGATIVE EQUITY: QUICK GUIDE
Negative equity is when the value of someone's home is less than the amount they owe on their mortgage
The Bank of England estimates that negative equity currently affects between 700,000 and 1.1 million UK households
Negative equity can make it harder to sell and move, or to borrow against the value of your home to pay off other debts, or to finance normal household spending during a period of unemployment
However, if you are not looking to move, negative equity is not necessarily a problem and can be overcome by waiting for the housing market to recover, while at the same time continuing to pay off your mortgage
Under its new arrangement, existing borrowers would take out a loan for 95% of the value of their new house at a fixed rate of 6.73% for three years or 7.48% for five years.
They would have to put down a 5% deposit from their own funds.
They would then be able to add on the negative equity from their old home, up to another 25% of the value of the new property, at a higher fixed rate of 7.23% for three years or 7.98% for five years.
As well as having their incomes and outgoings assessed by Nationwide, borrowers will also have to pass a stress test.
This will ensure they can still afford the mortgage repayments if interest rates have risen to 9% or 10% once the fixed-rate element of the loan has expired.
No takers yet
A Nationwide spokeswoman said although the deal was first made available in June, it was not being actively marketed.
So far none of its customers have taken up the offer.
It was, the spokeswoman said, aimed at helping only a few existing customers who came to the society and asked for help because they found they were in negative equity but were being forced to move house.
"Borrowers in these unique circumstances are simply able to transfer part of their existing negative equity with them when they need to move home - the actual value of the negative equity and the loan-to-value will reduce in all circumstances," she said.
"The borrowers have to meet our own affordability criteria," she added.
There has been much criticism of the loans above 100% that were available at the peak of the housing boom, which immediately placed borrowers in negative equity.
The most notorious were those offered by the now nationalised Northern Rock bank.
The Nationwide's deal was a "really consumer-friendly move" said Ray Boulger at mortgage broker John Charcol .
He added that at least two other major lenders were looking at introducing something similar for existing customers.
But financial planner Jonathan Davis, of Armstrong Davis, said the building society's new policy was a "joke", and that it exposed the lender to further losses if house prices continued to fall.
"You are taking people in negative equity, pushing more money down their throat to back an asset that is still going down in value," he said.
"All the banks and building societies thought they were going to get their money back when they lent gargantuan sums in the run-up to 2007 - they were clearly wrong then and they are wrong again," he added.