Control your emotions. This is extremely important. Most emotional response to conflict comes from personalizing the issue. The best way to remove emotions is to separate people issues from the problem at hand. However, if the issue is a people issue, make a point to deal with it separately and later.
When it appears there is no true impasse, nominate a third, but equal, party to resolve the conflict. The arbitrator can write up each side’s interests and offer solutions that are both agreed upon. The arbitrator should present both sides objectively and without prejudice for the purpose of coming to a resolution.
Take your personal stance into consideration. Are there specific people or issues that might set your off and make you handle conflict poorly? Examine the last few times you handled conflict poorly. Identify the common denominator in every situation. Are there common themes? Once you pinpoint the cause, mentally rehearse a better way to handle future situations.