As much as you want to supervise people who get along well all the time, the harsh truth is conflicts will erupt. And when they do, it's not necessarily your job to intervene.
In many cases, the best way to deal with bickering employees is to adopt a hands-off policy. Keep your distance. Let them resolve their own issues.
If you rush to referee every conflict, you may wind up breeding more conflicts. Employees may figure that they can get your attention by butting heads with a coworker, so conflicts can multiply. What's worse, your quick intervention to settle conflicts teaches employees that they need not take responsibility for getting along on their own.
Apply this test to determine whether to intervene in an employee conflict:
Defusing conflict requires skill and diplomacy, in part because your interest and your employees' interests often clash. Your goal is to reach a positive outcome so that the employees in conflict learn to get along (or at least stay out of each other's way). But many employees want you to play judge and jury--to study the cause of the conflict and assign blame to their adversary. In short, they are more intent on defending themselves while you simply want them to work together with civility.