There have been no new cases of Legionnaires' disease in the outbreak in the capital.
On Tuesday, the government announced a third man had died from the disease but said the numbers were falling.
Figures released on Wednesday show no new cases have been detected, leaving the total number at 99. Confirmed cases stand at 50, while suspected are at 49.
Two people are still being treated in intensive care and seven others are in hospital. 20 people are being treated at home and 57 have been discharged.
Three men have died in the outbreak, including Robert Air who was working on a building site in Gorgie when he contracted the disease.
The source of the outbreak is yet to be identified, but NHS Lothian have said it is most likely to have come from a cluster of cooling towers on Wheatfield Road in the south of the city.
Lothian and Borders Police and the HSE are investigating the three deaths.
Nicola Sturgeon said: "Strong evidence continues to suggest that the outbreak has peaked. NHS Lothian are maintaining high quality care for patients who remain unwell and work to identify and deal with the source of the outbreak continues."
More About Legionnaires' outbreak
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- Top professor backs call for public inquiry into Legionnaires' outbreak
- Legionnaires' outbreak: Patients take legal action to demand public inquiry
- Legionnaires': Health chiefs declare the capital outbreak over
- Legionnaires' outbreak: Another person confirmed as having the illness
- Legionnaires' outbreak: Another person confirmed as having the illness
- Legionnaires': Lack of new cases suggests outbreak has 'peaked'
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