The loans, only available to Nationwide customers moving home, will allow homeowners to borrow more than the value of the property they wish to buy.
Customers can take loans for 95% of the value of their new house but will also be able to carry up to 25% of the loss on their existing property. Borrowers will still need to provide a 5% deposit.
The loans are designed to help those who want to move house but are restricted by the potential loss.
The building society is not widely marketing the offer and says it does not expect huge demand.
There has been much criticism of home loans above 100%, which immediately placed homeowners in negative equity, since house prices began to fall steeply last year. Financial watchdog The Financial Services Authority is believed to be considering banning loans in excess of 100%.