Аннотация:In this paper we prove a countable set of non-Shannon-type linear information inequalities for entropies of discrete random variables, i.e., information inequalities which cannot be reduced to the “basic” inequality I(X:Y|Z)≥0. Our results generalize the inequalities of Z. Zhang and R. Yeung (1998) who found the first examples of non-Shannon-type information inequalities.