  Let $(R, \frak m)$ be a homomorphic image of a Cohen-Macaulay local ring and
$M$ a finitely generated $R$-module. We use the splitting of local cohomology
to shed a new light on the structure of non-Cohen-Macaulay modules. Namely, we
show that every finitely generated $R$-module $M$ is associated by a sequence
of invariant modules. This modules sequence expresses the deviation of $M$ with
the Cohen-Macaulay property. This result generalizes the unmixed theorem of
Cohen-Macaulayness for any finitely generated $R$-module. As an application we
construct a new extended degree in sense of Vasconcelos.
