Abstract. Let a be an ideal of a commutative Noetherian ring R and M a finitely generated R-module. Let t be a natural integer. It is shown that there is a finite subset X of SpecR, such that AssR(Ht a(M)) is contained in X union with the union of the sets AssR(Extj R(R/a,Hi a(M))), where 0 i < t and 0 j t2 + 1. As an immediate consequence, we deduce that the first non a-cofinite local cohomology module of M with respect to a has only finitely many associated prime ideals.
