The inevitable conflict that occurs in project management may not necessarily be a bad thing. Conflict occurs when individual goals or needs clash. One reason it is so common in project management is because projects often include people with different ideals and personalities. The term conflict generally carries a negative connotation however conflict can be constructive and serve to help to build relationships and improve team dynamics. The key is in the resolution of that conflict.
The project manager must be able to address problems while respecting individual differences. Maintaining good relationships should be a top priority. Be calm and treat one another courteously even if you are under a great deal of pressure.
Be careful not to confuse the person with the problem. Sometimes project managers believe people are just trying to be difficult when, in effect, they are making a valid argument. By listening carefully to the problem you end up debating real issues and have a better understanding of why the person has taken such a position. In addition, when you understand where the person is coming from you are better able to defend your position.
Revisit and agree on the project objectives then take a close look at the facts surrounding the situation. By working together you could find the answer lies in a third position involving compromise or in thinking outside the box. The fact that you arrived at this decision jointly will foster respect and help maintain or build a good relationship.