Hearts will face Edinburgh rivals Hibs in the next round of the Scottish Cup if they can make it by Raith Rovers.
The Tynecastle club were held 1-1 at Stark's Park on Sunday by the Ladbrokes Championship side, and will now go to a replay at Tynecastle this Wednesday.
Celtic have been drawn at home to Inverness in the fifth round, while Rangers will take on Jim Duffy's high-flying Morton.
A rather excitable Sir Rod Stewart and former Hibs boss Alan Stubbs conducted the draw in the immediate aftermath of Celtic's 3-0 win over Albion Rovers.
The pair almost plucked out an Old Firm game from the hat, however the Glasgow rivals have been kept apart for at least one more round.
There are also all Premiership ties away from Parkhead when St Johnstone take on Partick Thistle and Aberdeen travel to Ross County.
FULL DRAW:
Dunfermline Athletic v Hamilton
Raith Rovers/Hearts v Hibernian
St Johnstone v Partick Thistle
Ayr United/Queen's Park v Stirling Albion/Clyde
East Fife v St Mirren
Ross County v Aberdeen
Celtic v Inverness
Rangers v Morton
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