Sinn Fein's Gerry Adams and the DUP's Ian Paisley have had direct exchanges across the floor of the Northern Ireland Assembly.
The two party leaders debated the composition of the United Irishmen
The party leaders first debated the religious composition of the United Irishmen before moving onto wider political matters.
The debate was being held to discuss how proceedings on 24 November were handled by NI Secretary Peter Hain.
The motion had been tabled by Ulster Unionist leader Sir Reg Empey.
Sir Reg's motion, which was passed by the assembly, said Mr Hain had interfered in proceedings on that day when the DUP and Sinn Fein were asked to indicate their choices for first and deputy first minister.
During the debate, Mr Adams moved things on to the role played by Presbyterians and the rising of the United Irishmen.
The exchanges then moved to politics when Mr Adams objected to Mr Paisley using the term IRA/Sinn Fein.
"There is no party here called IRA/Sinn Fein, the party is Sinn Fein," he said.
But, Mr Paisley said the term IRA/Sinn Fein was used by more than his party.
"Evidently the members of the British government don't know it, the members of the Tory party don't know it - for that is how they refer to them."
BBC Northern Ireland political editor Mark Devenport said the exchanges were "feisty but fascinating" given the long-standing refusal by the DUP to exchange in any direct dialogue with republicans.
Monday's meeting was the first substantive debate of the transitional assembly, designed to deliver devolution by 26 March.
Peter Hain has come under criticism
The DUP is seeking delivery from Mr Hain on his economic package and other issues and from Sinn Fein on policing.
On Sunday, Ian Paisley Jr of the DUP said his party was not bothered about any power-sharing deadline or dates for devolving policing.
Mr Paisley said it was up to Sinn Fein to prove republican credentials and build confidence before any restoration of devolved government at Stormont.
He insisted Gerry Adams would not get a date from the DUP for the transfer of policing powers to Stormont.
The DUP leadership held a one-day meeting near Templepatrick on Friday to agree the party's strategy regarding power-sharing.
It followed claims of discontent among the ranks about aspects of the St Andrews Agreement which surfaced at the assembly on 24 November when the DUP and Sinn Fein were asked for ministerial nominations.
Proceedings were adjourned that day after an attack by loyalist Michael Stone.
After the adjournment, DUP leader Ian Paisley said that if all his conditions were fulfilled he would accept the first minister's post after a spring election.
Sinn Fein had nominated Martin McGuinness as deputy first minister.