The Magician displays a joker which is moved around the fanned reverse of the deck. The Spectator is instructed to call out stop and the joker is inserted. The deck is turned face up, still fanned, to show the joker sitting under the now selected card (For example the 2 of hearts)

 

The Joker is visibly removed and shown both sides. The cards are squared up. The magician (or the spectator) “removes” the “invisible” card (The chosen Card) The whole deck can be examined and the chosen card really has vanished. So cleanly.

 

The magician then makes it reappear anywhere he chooses.