  Spectrum of the Pauli projector of a quantum many-body system is studied. It
is proven that the kern of the complete many-body projector is identical to the
kern of the sum of two-body projectors. Since the kern of the many-body Pauli
projector defines an allowed subspace of the complete Hilbert space, it is
argued that a truncation of the many-body model space following the two-body
Pauli projectors is a natural way when solving the Schr\"{o}dinger equation for
the many-body system. These relations clarify a role of the many-body Pauli
forces in a multicluster system.
