Let R be a Noetherian ring, a be an ideal of R and M be a finitely generated R-module. The aim of this paper is to show that if t is the least integer such that neither H(a)(t)(M) nor supp(H(a)(t)(M)) is non-finite, then H(a)(t)(M) has finitely many associated primes. This combines the main results of Brodmann and Faghani and independently of Khashyarmanesh and Salarian.