  We prove that for arbitrary two finitely generated subgroups A and B having
infinite index in a free group F, there is a subgroup H of finite index in B
such that the subgroup generated by A and H has infinite index in F. The main
corollary of this theorem says that a noncyclic free group of finite rank
admits a faithful highly transitive action on an infinite set, whereas the
restriction of this action to any finitely generated subgroup of infinite index
in F has no infinite orbits.
