We show here how to define short exact sequences in pseudomodules. More precisely, for a given subpseudomodule M of a pseudomodule N, we define an equivalence relation such that the sequence , is (almost) exact. This then yields a decomposition of N into a subdirect sum of pseudomodules: . This approach generalizes that of [8], where the decomposition was limited to the case of pseudomodules with torsion.