Take a few deep breaths and close your eyes or go silent so you can try to get your anger under control.  Depending on how intense the argument is and how good you are at tempering your emotions in the moment, you may feel comfortable with resuming the discussion with the other person once you take a moment to try to calm down. Another approach may be to physically step away from the argument. Let the other person know you need a timeout or time away from the argument. Once you inform them you need to take a break, go into another room, excuse yourself from the table, or head out for a long walk or run.  An argument is a time of heightened emotions, so physically distancing yourself from the situation can help to put your emotions into perspective. But it's essential you let the other person know you need a time away to sort out your thoughts and emotions, and never simply storm off or walk out of the room with no explanation or promise to return to resolve the argument. If your anger can be charted on a scale, try to pause and calm down when your anger level is at a three or four, rather than a high 10. By the time you reach level four or higher on the anger scale, you may be so filled with rage or self indignation towards the other person you may end up saying more damaging and hurtful things to the other person. This will then likely make it more difficult to work on a mindful resolution of the argument later.  If an argument does reach a high 10 on the anger scale, and things are said that you or the other person will likely regret saying later, it's important to think about how this conflict will affect your relationship with this person. For partners who don't fight often, forgiveness may be the best way to resolve the argument, especially if it has escalated to a very angry or hurtful level.  Keep in mind that the idea of “fighting fair” is mostly an oxymoron in a relationship, like “jumbo shrimp” or “military intelligence”. A fight usually begins on uneven or unfair ground for both parties, so even if it does escalate to very angry levels, it's important to work towards forgiveness rather than holding a grudge or being passive aggressive about your anger. While this may sound like a tall order, especially if you're experiencing intense anger or anxiety due to the argument, it's important to return to your partner with a clear sense of what triggered the argument and how you are going to try to resolve the argument.  You can write down your feelings in a journal or diary. You can also try to listen to music to calm down and focus on processing your emotions. Another option might be talking aloud to yourself in an empty room or space. If you are having a hard time processing your emotions on your own, you may want to reach out to someone you trust and discuss your feelings with them before you return back to your partner. For example, a good friend, another family member, or professional help like a counselor, a therapist, or a spiritual guide. Often, when we are caught up in an argument, we focus on how we are feeling, as opposed to how the other person is feeling. The “need to be right” defense usually occurs because we are in fact afraid of being wrong or feel threatened by the other person's point of view. Think about how the other person may be feeling as a result of the argument. Consider if anything you said or did towards them could have acted as a trigger for their anger. Place yourself on the receiving end of your anger and think about how angry or upset you would be if you were in their position.

Summary:
Try to calm down. Work on ending the argument earlier, rather than later. Process your emotions. Talk to someone about your emotions. Consider the argument from the other person's point of view.