  In this paper biharmonic maps between doubly warped product manifolds are
studied. We show that the inclusion maps of Riemannian manifolds $B$ and $F$
into the doubly warped product $_{f}B\times_{b}F$ can not be proper biharmonic
maps. Also we analyze the conditions for the biharmonicity of projections
$_{f}B\times_{b}F\to B$ and $_{f}B\times_{b}F\to F$, respectively. Some
characterizations for non-harmonic biharmonic maps are given by using product
of harmonic maps and warping metric. Specially, in the case of $f=1$, the
results for warped product in \cite{Balmus-mont} are obtained.
