I had a fallout with my opposite gender friend (female) about 6 months ago. I wonder if there are any way I can let her know I am a better man (I am doing it for myself) without contact her?
It really depends on the situation or friendship. Is it a real life friendship or an online friendship? Do you have mutual friends? Mutual friends could help. I once had a falling out with a friend who that I played an online game with. We did not speak for several months but we both managed to make up and are still friends to this day, online, but have never met face to face. With real life friendships things could be touchy if there are things like a restraining order in place.
6 months is a pretty short time to become a "better man". She probably won't believe it. If she has told you not to contact her, maybe you should leave things alone until she contacts you. If you must contact her, you could write her a letter. A proper, snail-mail letter. Just don't expect a response.
If you are a better man then you should not have any problem making new friends and starting over! Sometimes it is best to let the past be the past and move on.
If she cares or wants to know that you've improved upon yourself, she will find out on her own. "Please do not contact me" means exactly what it says. Move on.
I haven't spoken to her for seven months. I have been trying new activities such as making new friends, having deeper friendship, going to the nude beach, seeking counselling, taking self-improvement courses such assertiveness, anger management, communication, money management. At the same time, I still miss her dearly. I found I cannot wait anymore, I wrote her a letter. I found out it is better then some of my destructive behaviors. "Everywhere I look something reminds me of her"