Adverb
square on (not comparable)
(idiomatic) accurately, correctly.
Death isn't enough. It doesn't remove the stain. But a slap, a whiplash, square on the face, does. Because a man's face is as sacred as his mother or his wife. Mario Vargas Llosa
I was the center square on Hollywood Squares for about fifteen weeks. Jerry Mathers
I would be good for maybe not the center square but an upper square on 'Hollywood Squares.' John Hodgman