There have been two new confirmed cases, taking the overall total to 41.
They were both previously classed as "suspected" and the number of suspected cases has therefore dropped from 49 on Tuesday to 47 yesterday.
So far 56-year-old Robert Air, from Seafield in Edinburgh, is the only person to have died in the outbreak.
The Health and Safety Executive and Edinburgh City Council are investigating the source of the outbreak.
Of the cases being treated in hospital, 11 are in intensive care and 19 on general wards. A total of 18 cases are being treated in the community, while 32 have been discharged. Seven are being treated outwith the NHS Lothian area.
Those confirmed as having the disease are aged from 33 and 81, with more men than women affected.
Health Secretary Nicola Sturgeon said: "These numbers again offer reassurance that the worst of the outbreak is over. The increase of confirmed cases and reduction in the suspected cases is in line with expectations. However, there is no room for complacency and we will continue to monitor the situation."