"How to Handle an Unusually Irritating Co-worker" means that you have to be self controlled and have a defense system to let the co-worker know that you are not coming to work everyday to be the brunt of condensations.  Before you approach the perpetrator, you need to not take the information coming from the coworker who is irritating  you, seriously.  If you take the irritating co worker seriously, then you would be giving credibility to the behavior to you.  You do not want to give an audience to someone who is constantly irritating you unless the behavior is an affront to your production at work.

You are not taking the co-worker seriously if you do not provide an audience and if you do not listen to what the person is saying.  If you are receptive to what the irritating co-worker is doing to you, then more often than not you are urging  continuance. Do not be receptive to irritating comments about yourself. If the personal comments is the cause of the irritation between your co-worker and you then there are some steps that you can take. 

You should strive everyway to outdistance the irritating coworker so that talk will be more on the positive aspects of your work instead of the irritating part. You can block the irritating remarks or behavior by providing an alternative forum of discussion.  Sometimes, you may be able to simply change the subject. The easiest thing to do, in fact,  is to move the topic of discussion and change the subject.  Do not add to the conversation or acknowledge that the irritating co working is seriously irritating you. There is no need to prolong a conversation that is not working optimal for you.

A more direct approach is to actually tell the co worker that you are being irritated by their behavior and that you would like to meet and talk on a more congenial forum.  You must rise above the situation and raise the bar abandoning any emotion that keeps telling you how much the co worker is irritating you.  You raise the bar by being the bigger person and talking to the coworker and let her know that you do not appreciate "sexist" jokes for an example.

If the irritating remarks is about your job then the conversation should be with your boss and not with your co worker.  Do not take the behavior seriously and direct your attention to the person who can provide you with comments that will help with your job performance.  It is not easy to ignore a person who is irritating you and the purpose of "How to Handle an Unusually Irritating Co-Worker" is not to suggest that you do.  If you ignore the irritating co-worker, it would be like you are accepting the irritating behavior.  By no means should you not bring the irritating situation up, initially with the perpetrator and then with the boss.

Sometimes it is better to have an intermediary solution such as a boss depending on what the problem is between the two employees.  The advice of not taking the irritating co-worker seriously gives you the objectivity to speak rational and with good common sense on what can be done so the two of you can get along together.

The boss is aware of the tension but the boss's  job is to keep the business sustainable and not to play a referee in a disagreement for example.  If the irritating co-worker is causing your work to be less than the best you can do, then you may need to bring the situation to the boss's attention.  Some remarks can not be brushed off and not taken seriously especially if something was said pertaining to your religion or creed.

The words "unusually irritating" means that the co worker has already ticked you off so you may have to bring the situation to the boss's attention.  If you are a person who do not like to let the boss know that you are having a working-together relationship problem, you may want to see if you can find a more suitable place to work.  It is not suggested that you choose the flight method of dealing with an unusually irritating co-worker, it is suggested that you do  find a way to be able to come to work without having to deal. 

The best case scenario in handling an unusually irritating co worker is to bring the incident to the co worker's attention and let him or her know to stop saying or doing what ever is bothering you.  I you just do not like the person's personality, then not much can be done about that except  to distance yourself from each other in the workplace.Stay professional in your delivery and do not make the offense sounds like it is doing anything except keeping you from being productive at work. 

Bringing the work related result of the unusually irritating co-worker may cause the person to think twice about what he or she is saying and doing and relinquish the action, words or behavior.  If you are not a confrontational person, and your work is being affected then your boss should be consulted for a viable solution.  Afterall it is the boss's job to see that each employee works to optimal levels in a comfortable non-hostile environment.  The boss may be able to come up with a good solution to the problem of the unusually irritating co worker.  However, do not use those terms in explaining the malfunctions of the co -worker relationship.  Be detailed in your delivery and speak to your boss face to face preferably with the co-worker in the meeting as well.