  A finite group $G$ is called monomial if every irreducible character of $G$
is induced from a linear character of some subgroup of $G$. One of the main
questions regarding monomial groups is whether or not a normal subgroup $N$ of
a monomial group $G$ is itself monomial. In the case that $G$ is a group of
even order, it has been proved (Dade, van der Waall) that $N$ need not be
monomial. Here we show that, if $G$ is a monomial group of order $p^aq^b$,
where $p$ and $q$ are distinct odd primes, then any normal subgroup $N$ of $G$
is also monomial.
