  A scalar field theory with a $\chi^\dag\chi\phi$ interaction is known to be
unstable. Yet it has been used frequently without any sign of instability in
standard text book examples and research articles. In order to reconcile these
seemingly conflicting results, we show that the theory is stable if the Fock
space of all intermediate states is limited to a {\em finite} number of
$\chi{\bar\chi}$ loops associated with field $\chi$ that appears quadradically
in the interaction, and that instability arises only when intermediate states
include these loops to all orders.
