Well, the back handspring step out is a skill used in the level 6 floor routine, and also used in a large amount of level 7 beam routines. The whole point of the skill is to do a backhandspring in a more interesting, elegant way. Here are some steps to do this skill:
1) You start off just like a normal backhandspring
2) As soon as your hands touch the ground/beam, split your legs with your good leg coming down first.
3) You should be able to hit a good split by the time you are ready to push off of the ground.
4) If you pause after your hands hit the ground, you are arching too much (sagging)
5) You are supposed to have a nice sharp pop off of the ground as soon as your hands touch the ground and your feet are heading the same way.
6) When your hands come off the ground, be sure to step your feet out into a good lunge, and to have your upper body lift up quickly.
So basically, over all, this skill is supposed to be smooth, fast, and done with straight knees and pointed toes.
-GCG