The ScotRail Alliance's poor punctuality has shown signs of finally being turned around with a third month of improvement and the best punctuality since September.
However, it is still slightly worse than a year ago and underlying performance by the partnership with track body Network Rail has yet to return to an upward trajectory.
The figures come after ScotRail was ordered to submit a remedial plan to ministers following dozens of cancellations a day caused by the late delivery of new trains and the knock-on effects of industrial action.
These have now been significantly reduced.
A total of 88.4 per cent of trains arrived within five minutes of time in the four weeks to last Saturday.
That compares to 84.2 per cent in the previous period in December, 83.4 per cent in November and 80.5 per cent in October.
However, the official industry comparison is with the same period last year, when it was 0.4 points better at 88.8 per cent.
The gains have also yet to improve the key measure of average punctuality over the last year, which was unchanged for a third month at 87.3 per cent.
That figure has not improved since falling from 91.2 per cent in August 2017 and ScotRail does not expect it to meet its 92 per cent target for another two years.
ScotRail was responsible for the most delays, such as from faulty trains, which accounted for 45.1 per cent of the total.
That compared to 35.7 per cent which were the responsibility of its Network Rail partners, such as track and signalling faults.
The alliance said the latest improvement had come despite it running 5 per cent more services - or 2,500 a month - such as on a new Edinburgh-Glasgow route via Cumbernauld, and on the east coast north of Edinburgh.
It said the biggest single causes of delays last month were a signal fault at Glasgow Central and a train fault near Haymarket in Edinburgh.
ScotRail Alliance operations director David Simpson said: “Everyone at the ScotRail Alliance is working flat out to improve punctuality for our customers, and it is a real positive to see performance continuing to show such significant improvement.
“We know this continues to be a challenging time, and there are areas where we need to deliver a better service, but things are moving in the right direction.
“The investment we are making in Scotland’s Railway is delivering more services than ever before and we are committed to giving our customers the service they expect and deserve.”