You can't remove it completely (I think), but you can move it down the list easily. Simply select Slot 1 and then try to equip an ability there that's already on the bar. It'll swap their positions around.
For example, if I'm a Marauder and I want to exchange Light Swing (Slot 1) with Heavy Swing (Slot 0) I would click on Slot 1 and then pick Heavy Swing from my abilities list. Light Swing will then be assigned to Slot 0 and Heavy Swing will move to Slot 1.
Naiya | Mithra | Windurst | Rank 10 | 1st Lieutenant | Ragnarok
WAR: 75 MNK: 75 SAM: 66
RotZ: O | CoP: O | ToAU: O | Apoch Nigh: O
Naiyah | B.Elf | 85 Rogue | Stormscale
Doubleday | B.Elf | 85 Paladin | Stormscale