Hearts, who beat Rangers on Saturday to record their fifth consecutive win, will play Hibernian at Easter Road on the weekend of January 10-11.
Monday's draw handed holders Rangers a trip to St Johnstone while Celtic also face Irn-Bru First Division opposition in the shape of Dundee at Parkhead.
Rangers needed penalties to knock out Saints in last season's semi-finals and face a tough test against a side leading their division.
Motherwell will play non-league opposition with Mark McGhee's men facing a trip to the winners of the third-round clash between Inverurie Locos and Vale of Leithen.
Lochee United, the only junior side in the draw, will host Kilmarnock if they beat Ayr in their rearranged tie, although an Ayrshire derby could be on the cards.
Falkirk host last season's runners-up, Queen of the South, while Aberdeen will travel to play Raith Rovers or Alloa.
Dundee United have an away game against former player Jim McInally's East Stirlingshire, who knocked out Livingston on Saturday.
In some of the other ties, St Mirren will play away against Edinburgh City or Brechin, Inverness will host Partick Thistle and Hamilton play Ross County or Dumbarton away.
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Last updated: 01 December 2008, 15:35
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