Ortho Tri-Cyclen Lo - Already Bleeding, can I skip?

I love everything about the pill Ortho Tri-Cyclen Lo, except that very often my period will start a week early, when I start the blue pills. I then bleed for a full period like normal, while taking a pill every day. The problem is, when I need to take the green sugar pills and have my period when it is actually due, I then have a second full period back-to-back with the first one. This is getting really repetitive and I'd like it to stop.
I wanted to know, that since I have already had a full period on the blue pills, if I could skip the green sugar pills and start a new pack? I have already had my period, why take the green ones as well?