The deal comes with a £95 booking fee and £1900 completion.
Accord has also cut its rates on other products by up to 0.4%.
The deals include three-year fixed rates starting at 3.39%, five-year fixed rates starting at 3.99% and 10-year fixed rates starting at 4.84%
The range also includes tracker and offset deals with a two-year tracker at 2.54% at a £95 booking fee and £1,900 completion fee.
There is also a two-year fixed rate offset mortgage at 4.44% with the a £95 booking fee and £900 completion fee.
The minimum loan size on its larger products has also been cut to £200,000 from £750,000.
Steve McAvan, product development manager at Accord, says: “Swap rates have fallen recently, allowing us the opportunity to launch some exceptionally competitive products. Our fixed rate deals offer great rates as well as peace of mind for borrowers looking for security and protection from future interest rate rises.
“As well as our fixed rate products, the new range carries a wide variety of other deals meaning we should have something for everyone and the reduction in the minimum loan on our larger loan mortgage range will mean these attractive rates are available to more borrowers too.”