Tough task for United
Dundee United have been drawn away to SPL champions Rangers in the Scottish Cup fifth round.
The tie is scheduled to be played at Ibrox on 4th February.
In other games, holders Celtic visit the winners of the Inverness Caledonian Thistle and Dunfermline Athletic replay while last year's runners-up Motherwell host Greenock Morton.
Both Edinburgh clubs also have home advantage as Hearts welcome St Johnstone and Hibernian play Dundee or Kilmarnock.
Otherwise, Aberdeen face Queen of the South at Pittodrie, Ross County go to Hamilton Academical or St Mirren and Falkirk visit Ayr United.