  Let $G$~be a real Lie group and let $G^\circ$ be the identity component
of~$G$. Let $G$~act on a $C^\infty$ real manifold~$M$. Assume the action is
$C^\infty$. Assume that the fixpoint set of any nontrivial element of~$G^\circ$
has empty interior in~$M$. Let $n:=\dim G$. Assume $n\ge1$. Let $F$ be the
frame bundle of~$M$ of order $n-1$. We prove: there exists a $G$-invariant
dense open subset~$Q$ of~$F$ such that the $G$-action on $Q$ has discrete
stabilizers.
