  Let $(R,\m)$ be a Noetherian local ring and $M$ a finitely generated
$R-$module with $\dim M=d.$ This paper is concerned with the following property
for the top local cohomology module $H^d_\m(M)$: $$\Ann (0:_{H^d_\m(M)}\p)=\p\
\text{for all prime ideals} \p\supseteq\Ann H^d_\m(M).$$ In this paper we will
show that this property is equivalent to the catenaricity of the unmixed
support $\Usupp M$ of $M$ which is defined by $\Usupp M=\Supp M/U_M(0)$, where
$U_M(0)$ is the largest submodule of $M$ of dimension less than $d.$ Some
characterizations of this property in terms of system of parameters as well as
the relation between the unmixed supports of $M$ and of the $\m$-adic
completion $\hat M$ are given.
