  We construct a simple algorithm to generate any CHSH type Bell inequality
involving a party with two local binary measurements from two CHSH type
inequalities without this party. The algorithm readily generalizes to
situations, where the additional observer uses three measurement settings.
There, each inequality involving the additional party is constructed from three
inequalities with this party excluded. With this generalization at hand, we
construct and analyze new symmetric inequalities for four observers and three
experimental settings per observer.
