The Northern Ireland economy is still in "a deep downturn", an Ulster Bank survey suggests.
Every month, the bank conducts a survey of a representative sample of firms.
The April survey, covering the first full month of lockdown, had the lowest ever economic activity result recorded here.
The May survey showed a slight improvement but was still the second weakest on record.
The bank's chief economist Richard Ramsey said: "Northern Ireland's private sector reported some easing in the record rates of decline witnessed in April across output, orders and employment.
"However, these improvements were relatively modest and perhaps weaker than anticipated."
Every month, the bank asks businesses about things such as new orders, exports and staffing.
This is used to create a numerical index with readings of more than 50 indicating expansion and under 50 indicating contraction.
In April, the headline seasonally-adjusted business activity index was just 8.3, by far its lowest ever reading, while the May figure was 18.9.
Mr Ramsey said the most encouraging sign in the survey was that 15% of manufacturing firms reported a rise in output in May relative to the previous month.
That may reflect the fact that some factories resumed operations in May.
However, these firms were outnumbered more than four-to-one by those indicating a decline in activity.
Mr Ramsey said services firms are faring less well than manufacturing, with just one in 20 reporting an increase in activity in May.
Meanwhile, almost three-quarters of firms within the services industry reported a fall in activity last month, down from 90% in April.