In this note we show that if I is an ideal of a Noetherian ring R and M is a finitely generated R-module, then for any minimax submodule N of H t I (M ) the R-module Hom R (R/I, H t I (M )/N ) is finitely generated, whenever the modules H 0 I (M ), H 1 I (M ), ..., H t−1 I (M ) are minimax. As a consequence, it follows that the associated primes of H t I (M )/N are finite. This generalizes the main result of Brodmann and Lashgari (2000) .