Multiple parakeet head pecking?

I've had my male parakeet, Azul, for about five years now. I realized he was lonely so I thought if I got him another birdie friend it might help. I bought Jasmine, about a month old female parakeet, a little over a week ago. When I put them in the same cage, I noticed Azul pecked her head a little bit. I was immediately worried and seperated them. Now they're in the same cage, and I've noticed Jasmine sometimes picks at his feathers too. Is this normal behavior? Should I just leave it alone and let them sort of figure it out on their own? And at what point should I seperate them?