We describe a method of extending Bell inequalities from n to n+ 1 parties and formulate sufficient conditions for our method to produce tight inequalities from tight inequalities. The method is nontrivial in the sense that the inequalities produced by it, when applied to entangled quantum states may be violated stronger than the original inequalities. In other words, the method is capable of generating inequalities which are more powerful indicators of nonclassical correlations than the original inequalities.