Dear Xiao Min,
I want to apologize for my behavior at yesterday's birthday party. I am embarrassed about my bad argument, and hope that you never keep my behavior in your mind. If there is anything I can do to make up for my deficiency, I will do my every effort to reduce the impact on you.
I am very regretful for my crude behavior. I swear to you that I will pay more attention to my behavior, and take concrete actions to prove that such things never happen the second time. I sincerely hope to have your forgiveness and expect this will not impair our friendship.
I have received your letter. From the letter I can see you self-blame and also feel your apology. I know who you are because we grew up together. Last night I think you were just drunk. I accept your apology and decided to forgive you. We are still friends. I think this incident will not affect our friendship.
I am willing to accept your apology, because you are a very people who pay attention to his words and deeds. But I also hope you can do as you have promised, and never make the same mistake again. I believe your behavior on the birthday was just an unexpected accident. I hope you can pay more attention to your behavior. But I am still your friend.