Once you've done all you can to improve your relationship with a difficult co-worker, you may find that the only thing left is to find ways to live with your workplace rival. In that case, the first thing to do is define and maintain your boundaries, both mentally and physically.
Start by finding ways to put actual space between you and your nemesis. Would it help to switch to a different cubicle? Is it possible to transfer to a different department? No matter what strategy you pursue, you'll need allies. If you haven't already done so, it's time to discreetly discuss the problem with a member of the human resources team. Your organization may have systems in place for resolving conflict and organizing teams based on personality or other measures of compatibility.
In coping with a bothersome co-worker, consider the consequences of not addressing the conflict. Can you somehow survive and be happy in your job, or will your spirit deteriorate until you're ready to leap from the tallest building? Answering this question can help clarify your needs and bring you closer to eliminating the strife [source: Webne-Behrman].
No matter what your strategy for coping with a difficult colleague, you'll probably continue to have some interaction with him or her, assuming you remain with the organization. Just remember to keep calm and be respectful. Getting visibly upset will only weaken your professional standing and make you look like a loose cannon [source: Pelusi].
Lastly -- and perhaps most importantly -- keep in mind that most people don't set out to be rude or challenging. Chances are the person with whom you have a conflict is eager to resolve things with you as well. There is also a good chance that a simple discussion will clear the air. This is because difficulty in professional relationships most often stems from the manner in which opinions are delivered rather than the opinions themselves.