Competition to attract current account customers and savers scouring for better returns is being ramped up as a new product paying 5% interest is set to be launched.
Experts said the returns on the first new account to be offered by TSB since its relaunch last autumn beat much of what is on offer in the savings market.
The new "plus" current account will give customers an interest rate of 5% on balances up to £2,000, has no monthly fee and requires minimum monthly deposits of £500.
Up to two of these accounts can be held per person, so in theory someone could have two accounts, each with £2,000 in them earning 5% interest.
People are not required to hold the new product as their main current account as TSB wants to encourage them to try out the brand.
Applicants will need to go "paperless" in terms of their statements and correspondence and will also need to register for internet banking to get the 5% rate. The money saved by doing this is helping TSB to offer its relatively high level of return.
Customers will still be able to manage the account in branch and over the phone as well as online.
Five years of ultra-low interest rates have given savers a tough time trying to find any accounts that give them real returns.
Comparing the new current account to what is available in the savings market, the top-paying easy access account currently pays a rate of 1.50% and is being offered by Britannia, according to the
"best buy" tables of financial information website Moneyfacts.
Building society Nationwide also offers a current account with a 5% interest rate on balances up to £2,500, but the rate on the FlexDirect account reverts to 1% after 12 months.
Rachel Springall, spokeswoman for Moneyfacts, said the interest rate offered on the new TSB account is likely to "cause a stir".
She said: "The account is very straightforward and is likely to attract not only banking customers after a fee-free account, but also savers who want to make the most of their money."
Ms Springall suggested some Nationwide customers nearing the end of their 5% bonus rate may be tempted to consider TSB.
She said: "They could keep earning 5% on their deposits, beating most savings accounts out there today."
The overdraft on the new TSB account has a £10 fee-free buffer and a rate of 19.94% after that. Switchers will get a fee-free overdraft for the first three months.
TSB reappeared on the high street last September as a standalone brand for the first time in 18 years after parent Lloyds Banking Group was forced to ditch 631 branches under European rules on state aid.
The bank's chief executive Paul Pester recently said he was "not surprised" some of its customers are upset after it recently came bottom in a customer satisfaction survey by consumer help website MoneySavingExpert.
The bank, which has suffered from some high-profile technical problems since splitting from Lloyds last September, has set itself "a mission to deliver the best customer experience in banking".
Competition between banks and building societies has been hotting up since the launch of a new customer guarantee last September which makes it easier for people to ditch their old current account provider and switch to a new one.
The guarantee has cut the length of time it takes to switch to up to seven working days and outgoing and incoming payments are automatically swapped over to the new account.
Marks & Spencer recently announced that it plans to launch its first "free" current account this summer, which will offer consumers a £100 gift voucher to switch to it as well as loyalty points which they can spend in its stores and an automatic £500 overdraft, the first £100 of which is interest free.