The numbers of newly confirmed and suspected cases rose by two in the 24 hours to midday yesterday, compared to the rapid rises seen at the height of the health scare last week.
It takes the total number of people who have contracted the disease since the first case was identified on May 31 to 82. This includes 15 patients currently in intensive care – unchanged from Saturday – and 26 who are being treated on general wards.
The figures also include 16 people being treated in the community, 19 who have recovered and been discharged from hospital, and labourer Robert Air, 56, who died last week.
Contaminated water vapour from cooling towers have been blamed for spreading the disease.
Health Secretary Nicola Sturgeon said: "These latest figures are reassuring and in line with expectations, and although it is too early to be definite they do suggest we are now in the later stages of this outbreak. All those involved are responding extremely well.
"NHS Lothian services are coping with the demands on them and the City of Edinburgh Council and the Health and Safety Executive continue to make significant progress in their investigation to identify the source."
Dr Duncan McCormick, Consultant in Public Health Medicine for NHS Lothian, added: "We are pleased with the slow down in the number of cases presenting and we hope this will continue over the coming days."
The Scottish Government's Resilience Room, which has been monitoring the outbreak, will meet again today
The North British Distillery in Gorgie, one of six sites being inspected for traces of the virus, has been closed temporarily after being issued with an improvement notice by the Health and Safety Executive.