RBS and NatWest have launched one-year-bonds paying 3.2% interest.
The one-year fix is one of the more competitive deals on the market, beating Santander, Northern Rock and HSBC's best buys.
The bonds are only available for a small window of time - until 12 August and the minimum required deposit is £5,000.
A two-year-fixed-rate bond paying 3.75% is also available, as well as a three-year-stepped-rate bond, which pays 2% for the first year, 4% in year two and 6% in the final year. These bonds also require a £5,000 deposit.
"As interest rates remain at an all-time low, these new highly competitive fixed rate bonds will guarantee consumers with one of the best returns on the high street today," says Phil Sheehy, head of savings at RBS and NatWest.
All of the bonds can be accessed online, by branch or phone.
Although competitive, the one-year-bond still lags behind a number of other accounts from Yorkshire Building Society, Barnsley Building Society, the Post Office and Britannia Building Society.
Its two-year fix however, is only beaten by the Post Office's two-year-online bond, paying 3.96%.
The start date of the bonds isn't until 22 August and deposits before then will only earn interest at 2%. The accounts are also only available to the banks' existing customers.
The banks' new launches come just days after Nationwide launched an 18-month fixed rate bond and prove the fixed-rate market is seeing a lot of activity, says Peter Chadborn, partner of IFA Plan Money.
"I suspect that the worrying effect of increasing inflation combined with frustratingly low interest rates has been the catalyst for a number of fixed-rate deposits coming to the market."
Despite the difficult savings environment, Brits are still managing to save the same amount of money or more than they did last year, research from Standard Life shows. Its findings reveal 41% of savers have squirreled as much away or more as they did last year.
John Lawson, head of pensions policy at Standard Life, says: "It is encouraging to see that even when the public is faced with increasing financial pressures, with inflation pressures and rising utility costs to name but a few, they're taking the sensible approach by saving their money."