Is there any way that anyone knows of to get through to someone that never thinks they do anything wrong?

One of my friends is like this and only because I love her like e Sister I ignore her. You have 2 choices really. You deal with it and learn to tune her our or you find a new friend? She will never admit that she is wrong and you'll waste your time. Next time say something such as " I know you will only flip this on me and I said my peace so if you want to rant about this then go do it elsewhere"When she starts just stare with no expression and give her such a lame look. Maybe if she knew it did not bother you she will shut up. I hope things work out for you. Email me if you need to talk. happy new year.

If your putting that much effort into it, then its not worth it! Just let her go, and don't talk to her for a while! Then see if it gets through to her.