Your question is about how to improve eye contact. So you make eye contact with a girl and when she looks at you back u look down and ? Walk past ? So basically ur question is about picking up women but .... Just looking at them ? I'm not sure.
Anyway. If your looking at them, in a very direct game type approach, and then when they look back (which is want you want) you avert. So your problem isn't a question of eye contact. It's a question of approach anxiety. Especially since the direct game approach requires her to make eye contact back (if you're not verbally opening).
So either you change your approach to a more indirect approach, just go up, fuck eye contact, and ask her a question, or opinion or whatever.
Or get over the "approach anxiety" when running direct game. Although I must say, it's really response anxiety since the opener is actually your eye contact and her response is making it back.
How to get over any sort of social anxiety?
1) get yourself into state
2) rationalise and get over your limiting beliefs
3) develop yourself so you have more things to be self assured about
4) just do it
And what's the best way out of a situation where are girl catches you staring and u don't want to open. Just smile. Nod. Whatever. How do u behave normally in a normal situation. Just be friendly.
Translation.
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