Bognor, of National League South, will visit fellow NLS side Oxford City - ironically the team they were due to play the same weekend in the league.
The Rocks beat Oxford City 4-2 in the third qualifying round two years ago at Nyewood Lane. The sides are 18th and 19th in the league at the moment and have found their FA Cup runs a nice distraction from league struggles.
Bognor won 2-0 at Eastbourne on Saturday to reach this stage. They'll go to Oxford knowing it's 22 years since they last made the first round proper.
Burgess Hill, who play in the Bostik Premier one league below Bognor, have also been drawn to face NLS opposition - Dartford. The Darts are fifth in their division and will be tough opposition, though the Hillians can take heart from beating Wealdstone, also of NLS, in the third qualifying round.
The games will be played on Saturday, October 14, or Sunday 15. Prize money goes up nicely at this stage. Bognor and Burgess Hill have already netted Â£7,500 each for their third qualifying round wins and it's a Â£12,500 prize pot up for grabs for winners in the next round.
And of course the big incentive for the next round is that winners go into the first round proper, where they stand a chance of being paired with League One or League Two clubs and the prospect of a live BBC TV or BT Sport date, itself worth thousands more.
The draw was made live on Ray Stubbs' show on Talksport 2 with non-league legend Tony Incenzo helping to oversee proceedings.