The changes will come into effect from 1 August.
On the two-year fixed rate side, its deal at 60% loan to value (LTV) will fall by around 0.21% to 3.81%, while its deal at 75% LTV will decrease by 0.19% to 4.03%.
At 80% LTV, its two-year fixed rate will go down by 0.19% to 4.26%, and at 90% LTV, the rate will fall by 0.28% to 4.72%.
Halifax’s five-year fixed rate at 60% LTV will decrease by 0.1% to 4.01%, and at 75% LTV, it will go down by 0.15% to 4.03%.
Going up to 80% LTV, the five-year fixed rate will reduce by 0.16% to 4.21%, along with its deal at 85% LTV, which will stand at 4.21%.
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At 90% LTV, its five-year fixed rate will fall by 0.2% to 4.37%.
All the above deals have a £999 fee.
Last month, Halifax cut rates by as much as 0.1% on selected fixed deals for homemovers and first-time buyers.
Principality BS changes rates by up to 0.28%
Principality Building Society will lower selected rates and increase selected rates by up to 0.28% from 4 August.
On the rate decrease side, the five-year fixed residential rate at 80% LTV with a £1,395 fee will go down by 0.04%.
The firm’s residential cashback two-year fixed rate at 65% LTV and five-year fixed rate at 80% LTV will decrease by 0.03% and 0.02% respectively.
Looking at the rate increase side, residential rates between 65% and 95% LTV will rise by up to 0.28%.
Residential cashback products between 80% and 90% LTV will rise by around 0.12% and selected joint borrower sole proprietor (JBSP) deals at 75-90% LTV will increase by 0.07%.
Two- and five-year fixed shared ownership rates at 95% LTV will go up by around 0.1%.
Help to Buy Wales five-year fixed rates at 75% LTV will increase by up to 0.1% and buy-to-let (BTL) fixed rates between 60% and 75% LTV will go up by 0.07%.
Two- and five-year fixed holiday let rates at 60% LTV and 75% LTV will rise by 0.05%.