Can a wireless Xbox 360 controller be reprogammed to play on a different 360 console?

this contorler have to conect with you xbox but the is a small button on the front of your xbox with 3 cuved lines eg ))) same as you con troler wich is on the front left side of your controler they have to be bothh pressed or else it dont work but if you have a charge and play kit it automaticaly conncet if u plug ur contoler in. :) i also