In the middle of F1->H4, can I apply for H1?

[wangmouse]

I am in the middle of changing my status to H4 from F1 and haven't got the approval notice (receipt date is April 25, 03) yet. Now I got a job offer and the company can sponsor H1B and want me to start early sep. Can I apply for H1B though I haven't got my H4 approved? How can I do it?

Thanks a lot.