It will also be the first time the two have played in the Scottish Cup since 2009. Here are the last 11 meetings of the sides in pictures.
9. Hearts 0-1 Falkirk 7/2/09
The last time the sides met in the Scottish Cup was decided by a Steve Lovell header at Tynecastle as Falkirk marched on to that season's final Photo: Jarek Bogdanowicz
10. Hearts 2-1 Falkirk 13/9/08
Steve Lovell gave Falkirk a 16th minute lead at Tynecastle but it only lasted two minutes before Bruno Aguiar brought the hosts level. Andy Driver's second half goal then won the game for the Jambos Photo: Ian Georgeson
11. Falkirk 4-3 Hearts 21/09/10
A dramatic win in the Co-operative Insurance League Cup came for the Bairns over the ten men of Hearts courtesy of a Mark Stewart goal in the fourth minutes of added time Photo: Gary Hutchison