Be Open to Compromise
Holding desperately to a dogmatic grudge isn't likely to yield many benefits in a workplace conflict. And presenting a conflict as a black-or-white, right-or-wrong situation heightens tension and ensures that your co-workers will become exasperated with you in a hurry.
Stubbornness also signals to the other person that you have no intention of listening to his or her side of the story. Don't approach a meeting with this kind of take-no-prisoners mentality.
Instead, show that you are willing to give up ground on certain aspects of a disagreement. Your willingness to compromise demonstrates that you aren't letting negative emotions dictate your behavior or hamper professional objectivity.
If you have a hard time respecting your co-worker's viewpoint, remember that your position is unlikely to be the best overall solution to the situation, regardless of what you might think. Your infallibility on a contentious issue is even unlikelier to objective observers. In short, a win-win compromise is the best solution for everyone involved.