Loads of workplace conflicts go unsolved because of a lack of procedure for both parties involved. If you're in charge and have to solve a quarrel between two employees, you should have the penalties defined beforehand for the person in the wrong. Furthermore, in case of wrongful accusations, there's should also be some sort of consequences for the person making them as well. By defining a certain set of regulations within the workplace, you'll make sure that people know what wrongful accusations will do for them and their future in the company.
It's extremely important that, before you make any sort of decision, you give both parties an equal chance to present their case. A lot of hostility in the workplace comes because of exaggeration and false accusations. Don't react to anything before listening to both sides of the story. Ask various questions to understand the whole story. It's important that you grasp the perspective of both individuals. Otherwise, you could end up penalizing the wrong person.