The four cells farthest from the starting area are the promotion zone. When a player moves a pawn to one of these cells, e must choose to change it into a rook, knight, or bishop. There is no initial double move. This prevents the capture that could otherwise occur on the first turn. The king moves one square in any direction a bishop or rook can move.
All rules regarding check and mate are the same as in standard chess.
There is no castling move. Aside from the unusual board and piece moves, all rules are the same as standard chess. Of course, not content to leave well enough alone, I created a rather different game based on this one that is my real submission to the 39-square contest.