The "moving annual average" - on which the train operator is measured by ministers - increased by 0.3 points on the previous month.
It showed 87.6 per cent of trains arrived within five minutes of time over the year to 2 March.
Train punctuality in February - the "public performance measure" (PPM) - was also up for the fourth month in a row, to 89.8 per cent.
That compares to 86.6 per cent in the same period last year, and 88.4 per cent in January.
ScotRail said the latest figures showed that "more trains arrive on time than ever before" because it ran more trains in February than previously.
A spokesman said: "With the December timetable bringing more than 100 additional daily services for customers, it means more trains arrived within PPM than in any other previous four-week period since the start of the franchise [in 2015] – 55,927."
However, watchdog Transport Focus said that could mislead passengers.
Senior stakeholder manager Robert Samson said: "That tends to be 'industry speak' that we can understand, but the passenger will read [it as] 'more trains arriving on time and punctuality is improving'."
ScotRail has also been ordered by ministers to introduce two remedial plans to improve performance - over high cancellation levels on commuter lines into Edinburgh and near record-low passenger satisfaction ratings.
ScotRail said trains serving the main part of Glasgow Central - Scotland's busiest station - recorded their best punctuality for 18 months, of 95.7 per cent.
It said incidents that had the most impact on the performance of the ScotRail Alliance with Network Rail Scotland were a train fault near Edinburgh Waverley and a signal fault at Haymarket in the capital.
ScotRail Alliance managing director Alex Hynes said: “This has been a particularly encouraging period of performance, with the investment we are making in Scotland’s railway delivering significant improvements for our customers.
“We know there are still areas where we need to improve, but everyone at the ScotRail Alliance is working flat out to deliver the service that customers expect and deserve.”
But Scottish Liberal Democrat transport spokesperson Mike Rumbles said: “These performance figures are terrible.
“Services have been deteriorating for too long and the Scottish Government has done nothing to improve matters.
“Instead of putting all their efforts into avoiding bad headlines, by removing penalties for poor performance and letting Abellio off the hook, ministers should use the powers they have to improve the situation for passengers.”
A spokesperson for the Scottish Government’s Transport Scotland agency, which oversees the ScotRail franchise, said: “ScotRail’s continued improved performance for a fourth consecutive period is welcome news for passengers.
“It represents a small step towards the long-term positive change everyone expects and deserves.
“There is still work to be done, particularly in the east, therefore ScotRail’s focus must remain on delivering a robust remedial plan which puts passenger interests at the forefront of restoring performance to a high standard.”