The former Royal Bank of Scotland building in the heart of the square has been empty since restaurant chain Zizzi closed a branch there.
Now people have been sharing pictures of the building covered in graffiti and calling for action to be taken to fix it.
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Social media users described the graffiti on the A-listed building as “appalling” and “horrendous”.


Glasgow council response
Councillor Angus Miller, representative for Anderston, City and Yorkhill, said he had been in contact with Glasgow City Council about the graffiti problem in the area, but that work might require engagement with the owners.
A Glasgow City Council spokesperson told GlasgowWorld that graffiti on private property is the responsibility of the owner.
Plans for the building
We revealed last year that Viva Italia had submitted plans to carry out internal changes in the building.
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Since then, social media pages have been promoting Banca di Roma, an Italian restaurant which is set to move in at 31 Royal Exchange Square.
The Instagram page for the restaurant has only issued teasers.
One post said: “Our location. An iconic and grand vista reflecting our essence. Are you ready to discover Banca Di Roma?”
Another added: “Elegant, modern and stylish. A place to be surprised.”