Don't be so competitive! You don't have to try to be better than her in the things you do. The better person should be able to walk away from the other. But stopping your competitive behavior does not mean that you are weaker - in fact it makes you stronger. If it's difficult to do, find a way to be competitive secretly (remember it's not a secret if someone knows!) while you are alone. For example, if she is athletic, instead of competitively racing her, go to the gym and focus on becoming stronger than her, but don't tell anyone that is the reason you are doing it, and go by yourself. When you're around her be really nice - give her a high-five and admire how much stronger your arms look than hers. It will make yourself feel good without making anyone feel bad if you keep it to yourself.
