The banking group at the centre of the NatWest IT meltdown has raised hopes that it is finally getting to grips with the crisis.
RBS Group said the vast majority of NatWest and RBS accounts had now been free from disruption for two days as it works to clear up the chaos left by its IT failure last Tuesday night.
However it is still having greater difficulty restoring problems for its Ulster Bank customers, but a solution applied to the other two banks was successfully applied to Ulster Bank overnight.
It also said it is making progress in whittling down the numbers of remaining customers who are still experiencing problems.
The beleaguered banking group has scrapped its corporate hospitality at Wimbledon as it grapples with problems which have left some customers in limbo for more than a week, with some unable to access their wages and others facing delays moving home or disrupted holidays.
RBS Group said in a statement: "Account balances have registered as normal for the vast majority of RBS and NatWest customers over the last two days.
"We can also confirm that the small amount of outstanding unprocessed transactions continues to reduce, and significant further progress is expected today.
"As previously cautioned, however, progress towards a completely normal service is likely to be affected by the significant stress on the system over recent days."
The group said that while Ulster Bank customers are likely to continue facing "significant problems" for the rest of this week, the success of Tuesday night's IT solution had increased its confidence that it will restore a full service by Monday.
It added: "We apologise once again for the unacceptable service customers have experienced and thank them for their patience."