The Scottish Secretary Alister Jack has said "one of the left-wing" bank holidays could be replaced with a "Union Day".
Jack, the MP for , was on a panel answering questions at the conference in about ways to strengthen the union between Scotland and England.
During the event he was quizzed if the government should create a Union Day bank holiday.
He asked: "Are we replacing it with another bank holiday by any chance?"
When pushed on his answer by the panel chair, said: "Yes, we could get rid of one of the left-wing ones."
After a burst of laughter from the crowd, he added: "Bring in a Union Day."
The comments come after Jack said the Scots Tories have been brought into line with the UK government after interim leader Jackson Carlaw reversed their opposition to a no-deal Brexit.
Today is the final day of the conference which sees primer minister Boris Johnson give his keynote speech.