Barnet will host either Coalville Town or Grimsby Town in the FA Trophy second round.
The Bees made it through to the second stage after claiming a 1-0 away victory against Hayes & Yeading on Saturday.
Coalville and Grimsby played out a 1-1 draw and will face each other in a replay at Blundell Park on Tuesday evening.
The second round tie will be played on Saturday, December 14 and will mean the Bees' Skrill Premier fixture against Aldershot Town will be rearranged.
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