  In this work we prove, in full details, that any finite dimensional
$C^*$-quantum groupoid can be deformed in order that the square of the antipode
is the identity on the base. We also prove that for any $C^*$-quantum groupoid
with non abelian base, there is uncountably many $C^*$-quantum groupoids with
the same underlying algebra structure but which are not isomorphic to it. In
fact, the $C^*$-quantum groupoids are closed in an analog of the procedure
presented by D.Nikshych ([N] 3.7) in a more general situation.
