I saw very early on in my straight shaving career this way to hold the razor from an old barber shop book. I haven't seen many people talk about this, so thought I would point it out. Once I switched to this grip, I noticed I had much better control of the full length of the razor, and my shaves improved. So, at least for the N-S pass, this is how I hold the razor.
Let me know if you have any questions
shave well
Drew