If the shoulders rotate more around the spine in putting... rather than ROCK up and down... the head will stay still... according to Mr. Utley. I tried this and found it to be pretty true. This goes along with the ARC stroke, or putting on an INCLINED PLANE.
Putting UP AND DOWN THE LINE tends to promote a rocking of the shoulders up and down... and often the head goes backwards on the down stroke. I have seen some very good players do it this way, however. Loren Roberts putts up and down the line.