  Within the decoherence theory we investigate the physical background of the
condition of the separability (diagonalizability in noncorrelated basis) of the
interaction Hamiltonian of the composite system, "system plus environment". It
proves that the condition of the separability may serve as a criterion for
defining "system", but so that "system" cannot be defined unless it is
simultaneously defined with its "environment". When extended to a set of the
mutually interacting composite systems, this result implies that the
separability conditions of the local interactions are mutually tied. The task
of defining "system" (and "environment") via investigating the separability of
the Hamiltonian is a sort of the inverse task of the decoherence theory. A
simple example of doing the task is given.
