  We give a handy way to have a situation that the $kG$-Scott module with
vertex $P$ remains indecomposable under taking the Brauer construction for any
subgroup $Q$ of $P$ as $k[Q\,C_G(Q)]$-module, where $k$ is a field of
characteristic $p>0$. The motivation is that the Brauer indecomposability of a
$p$-permutation bimodule is one of the key steps in order to obtain a splendid
stable equivalence of Morita type by making use of the gluing method, that then
can possibly lift to a splendid derived equivalence. Further our result
explains a hidden reason why the Brauer indecomposability of the Scott module
fails in Ishioka's recent examples.
