The draw for the competition, sponsored by Cooperative Insurance was made in the Hampden Museum earlier today - also sends Celtic to Kilmarnock in what is, on paper at least, the tie of the round.
Dunfermline Athletic, the only lower league side left in the tournament, will travel to Tannadice.
Cup Holders Rangers will surely be happy with a home draw, after their narrow escape at Firhill last night.
The full draw is as follows:
Falkirk v Inverness Caledonian Thistle
Rangers v Hamilton Academical
Kilmarnock v Celtic
Dundee United v Dunfermline Athletic