I haven't thought about folding paper airplanes in a lot of years. But I went and looked over the page after your comment, and as it turns out I used to fold something really similar. The main difference being, I didn't cut any corners in step one, and folded the two top corners all the way to the center fold in step four. Then folded that triangle that's left over the folds from step four.

I hadn't thought about that in as long as I can remember.