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This time the individual has somehow scaled the Church of Christ Community on the corner of St Andrew and Filleul Sts and placed a cone on top its spire.
A police spokeswoman said they "strongly" discouraged the behaviour.
"Depending on the situation, a person could face charges – such as wilful trespass, burglary or wilful damage.
"They are also potentially putting themselves in danger."
Anyone with immediate concerns about the safety of any person or property was asked to call police on 111.
Earlier this year a cone was placed in similarly precarious position atop the Fortune Theatre.
At the time marketing and communications manager Jordan Dickson said the road cone placed on top of the building "appeared out of the blue", staff having discovered it when they arrived at the theatre on Monday morning.
Staff were unsure who was responsible, but Mr Dickson said he had heard some speculation.
"I did hear someone say it might have been some very very brave student, but I have no clue."
An "intrepid urban explorer" had probably made the climb, Mr Dickson said.
The person in question must have been "pretty keen" to complete the task, he said.
He was unsure what route the person responsible had taken to get up there, but he suspected they might have used the scaffolding on the Corso Centre building next door to the theatre, which is being renovated.
"Maybe it was an opportune moment."