Collapsing masonry and scaffolding on the former Post Office headquarters at the West Port in Edinburgh has left nearby roads closed to access.
An eyewitness reported that scaffolding collapsed on the site
Police said there was no risk to the public or demolition workers when the masonry and scaffolding fell at about 1530 BST on Saturday.
Police officers were already on patrol at the site following the collapse of part of the building's floor on Monday.
The building, near the Grassmarket, is currently being demolished.
Some nearby roads, including the Grassmarket, are closed to traffic and Upper Lady Lawson Street has been closed to pedestrian access.
A spokesman for Lothian and Borders police said that there had been no danger to workmen or public.
He added: "The crashing was part of a controlled demolition although it came out further than anticipated."
An eyewitness said that a large part of the facade and some of the inner part of the building had collapsed.
She said: "They appear to have been caught off-guard."
Building control department experts are supervising the demolition of the last four floors of the building, according to an Edinburgh City council spokesperson.