  Let $p,q$ be prime numbers with $p^4<q$, and $k$ an algebraically closed
field of characteristic 0. We show that semisimple Hopf algebras of dimension
$p^2q^2$ can be constructed either from group algebras and their duals by means
of extensions, or from Radford biproduct $R#kG$, where $kG$ is the group
algebra of group $G$ of order $p^2$, $R$ is a semisimple Yetter-Drinfeld Hopf
algebra in ${}^{kG}_{kG}\mathcal{YD}$ of dimension $q^2$. As an application,
the special case that the structure of semisimple Hopf algebras of dimension
$4q^2$ is given.
