Work your handstand

The most commonly seen handstand pushup is the version facing away from the wall. However, when done incorrectly, this teaches an overextended back position and an incorrect pushup position. The first piece of any handstand progression is developing a hollow body position where you are able to maintain a neutral spine. (hollow rocks anyone?)  Once you can maintain a neutral spine while on the ground, it is time to start practicing the hollow position while inverted.