Dr Duncan McCormick from NHS Lothian told ITV News that although all the evidence points towards 'no further exposure' to the Legionella infection, those with underlying health problems who are already affected will take longer to recover.
NHS Lothian report that the number of confirmed cases is still 41, with 48 suspected cases, taking the total number of overall cases to 89.
A second person was confirmed dead after contracting the disease in Edinburgh, but has not yet been named.
The Scottish Health Secretary says there are 24 confirmed and 37 suspected cases of Legionnaires' disease. She expects this figure to rise.
Legionnaires' is a disease that strikes fear in people and its history shows it can be deadly.
The Scottish Health Secretary will today update MSPs on efforts to deal with a deadly outbreak of Legionnaires' disease in Edinburgh.