You cannot make a new faction while IN a faction. At the very least, you will have to leave your current faction in order to create a faction. Since you also need at least 5 people to start a faction, my suggestion is to find 6, and make one of them your nominee and Leader of that new faction. Have them makeover ownership of the faction to you and then it's your faction, you're still in your current faction.
Kay, I don't believe you need to join the faction you're creating. I was under the impression that the first person invited to the faction would end up being the leader if you're not present, though that might be wrong.