Hoops hope to cash in with a Diamonds tie
Celtic will begin their defence of the William Hill Scottish Cup at home to Airdrie.
Old Firm rivals Rangers, meanwhile, were handed an away trip to Cowdenbeath when the fourth round draw was made at Hampden last night with the help of Dave Mackay and Josh Taylor.
Dave captained St Johnstone to their first-ever Scottish Cup triumph, with Saints 2-0 winners over Dundee United back in 2014.
“Tartan Tornado” Josh, meanwhile, is one of boxing’s rising stars and is fresh from defeating Ryan Martin at the SSE Hydro to clinch a deserved victory in the Super Series quarter-final.
That has set him up with and set up a semi-final showdown with IBF champion Ivan Baranchyk.
The pair pulled out some knock-out ties.
There are two all-premiership matches to be played on the weekend of January 19-20.
Hearts will host Livingston, while Hamilton Accies will travel to Perth to face St Johnstone.
Meanwhile, Ayr United, 3-0 winners away to Beith yesterday, have been handed another derby against a team from the Ayrshire junior ranks.
They were handed a trip to face Auchinleck Talbot, who will be appearing at this stage of the competition for only the second time.
The full draw is –
Aberdeen v Stenhousemuir. Auchinleck Talbot v Ayr United. Celtic v Airdrie. Cowdenbeath v Rangers. Dundee v Queen of the South. East Fife v Morton or Peterhead. Edinburgh City or Inverness CT v East Kilbride.
Hearts v Livingston. Hibernian v Elgin City. Kilmarnock v Forfar Athletic. Montrose or Annan Athletic v Dundee United. Motherwell v Ross County. Partick Thistle v Stranraer. Raith Rovers v Dunfermline Athletic. St Johnstone v Hamilton Accies. St Mirren v Alloa Athletic.