  Let $G$ be a finite solvable group and $H$ a non-normal core-free subgroup of
$G$. We show that if the normalizer of any non-trivial normal subgroup of
$Fit(H)$ is equal $H$, then $H$ has a nilpotent normal complement $K$ such that
$G=KH$ and $KZ(Fit(H))$ is a Frobenius group.
