Eight wards remain closed at Renfrewshire hospital following the deaths of four patients who were being treated for a diarrhoea and vomiting bug.
A total of 24 patients are showing symptoms of Norovirus at the Royal Alexandra Hospital in Paisley.
Last week two people suffering from diarrhoea and vomiting died in the at RAH.
NHS Greater Glasgow and Clyde said the deaths, which had all taken place since Friday, were due to underlying medical conditions.
Norovirus was a contributory factor in one death.
Consultant microbiologist Dr Teresa Inkster said: "Norovirus has a sudden onset and can spread quickly. We would urge relatives and any visitors who have experienced diarrhoea or vomiting within the last 48 hours not to visit the hospital.
"We would also ask that visitors are restricted to close family and friends."
Meanwhile, visitors to two Highland hospitals have been asked to restrict their visits because of the bug.
Raigmore Hospital in Inverness has two wards closed to new patients, while a ward at Caithness General has also been shut, with visitors asked to stay away.
A spokesman said some of the cases had been identified as the Norovirus.
Scottish Labour MSP for the West of Scotland, Neil Bibby, said: "With eight wards now closed [at the RAH], the community needs an assurance that this outbreak is under control.
"Infection control practices need to be rigorously observed so patients and their families can have confidence when they go into hospital."