How do I create vertices that form square faces on a rectangle? I need to do this so I can build terrain properly.

This is what I am trying to get square faces on:



I tried deleting everything but the corners and this happens:



And this is what I want, square faces:
I'm curious about how come you have to start from this topology? 

In this particular case though, you could:




Select a vertical edge, and ShiftG > Select Similar > Direction
CtrlI (Select Inverse)
X > Limited Dissolve the now selected edges