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1) Be willing to separate rivaling employees. This requires minimal managerial exertion. Consider that some personalities may grate on the nerves of some. Often rivaling employees just don't like each other.
2) Know your limits. If it has become a major disruption, consider having a simple, private discussion with each of the rivaling employees. Don't make a big deal out of a small matter but don't ignore a spreading cancer, either.
3) Don't strive for perfect fairness. Don't expect yourself to be perfectly "fair." Rather, strive to treat employees impartially. If employees cry "Unfair!" tell them they do not have, nor are privy to, all the information that went into your decision. Be unemotional, calm, deliberate and firm.
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