  We show that if $\AA$ is a Fell bundle over a locally compact group $G$, then
there is a natural coaction $\delta$ of $G$ on the Fell-bundle $C^*$-algebra
$C^*(G,\AA)$ such that if $\hat{\delta}$ is the dual action of $G$ on the
crossed product $C^*(G,\AA) \rtimes_{\delta} G$, then the full crossed product
$(C^*(G,\AA) \rtimes_{\delta}G)\rtimes_{\hat{\delta}}G$ is canonically
isomorphic to $C^*(G,\AA) \otimes\KK(L^2(G))$. Hence the coaction $\delta$ is
maximal.
