  We show that a quantum system with nonlocal interaction can have bound states
of unusual type (isolated states (IS)). IS is a bound state that do not
generate a $S$-matrix pole. IS can have positive as well as negative energy and
can be treated as a generalization of bound states embedded in continuum on the
case of discrete spectrum states. Formation of IS in the spectrum of quantum
system is studied using a simple rank--2 separable potential with harmonic
oscillator formfactors. Some physical applications are discussed, in
particular, we propose separable $NN$ potential that describes not only most
important two-nucleon data (deuteron binding energy and s-wave triplet and
singlet scattering phases) but also the trinucleon binding energy without
making use of three-body forces.
