William Hill Scottish Cup holders St Johnstone will begin the defence of their trophy with a home tie against fellow Premiership side Ross County.
The match at McDiarmid Park is one of five all-Premiership ties drawn at the Scottish Football Hall of Fame, including a trip to Dens Park for Aberdeen to face Dundee and Partick Thistle hosting high-flying Hamilton Academical.
Elsewhere, Rangers have been drawn at home to Kilmarnock, and Championship leaders Hearts will play Celtic at Tynecastle in a repeat of last season's fourth round clash.
Should junior side Hurlford United defeat Stirling Albion in a replay they will face Raith Rovers, while Lowland League outfit Spartans have been rewarded with a home tie against either Greenock Morton or Airdrieonians after knocking out Clyde on Saturday.
Highland League champions Brora Rangers, who defeated Edinburgh City on Saturday, travel to Dumfries to face Queen of the South.
William Hill Scottish Cup fourth round ties:
St Johnstone vs Ross County
St Mirren vs Inverness Caledonian Thistle
Hurlford United/Stirling Albion vs Raith Rovers
Rangers vs Kilmarnock
Heart of Midlothian vs Celtic
Queen of the South vs Brora Rangers
Stranraer vs Dunfermline Athletic
Elgin City/Bo’ness United vs Arbroath
Falkirk vs Cowdenbeath
Spartans vs Greenock Morton/Airdrieonians
Berwick Rangers vs Albion Rovers
Dundee vs Aberdeen
Annan Athletic vs Brechin City
Ayr United/Alloa Athletic vs Hibernian
Motherwell vs Dundee United
Partick Thistle vs Hamilton Academical
Matches will take place the weekend of Saturday 29th November, 2014.
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