I' not sure which drill book you go by, but according to the Marine Corp and Navy Ceremonies Manual (MCPO 2560.20 [these numbers are close, but incorrect for me, can't remember them, sorry]), the instructions are to leave your right hand alone. Your feet spread normal distance and your hand moves to the flat of your back as normal. BUT, as of May 2003, the drill manual had a Significant Change. Your left hand should come to the cup in front of your body and rest holding it, with your thumb inside the cup. (This is from order colors. You cannot go to parade rest from Carry, as with the Manual of Arms.)