  We shall introduce a notion of free coactions of a finite dimensional
$C^*$-Hopf algebra on a $C^*$-algebra modifying a notion of free actions of a
discrete group on a $C^*$-algebra and we shall study several properties on
coactions of a finite dimensional $C^*$-Hopf algebra on $C^*$-algebras, which
are relating to strong Morita equivalence for inclusions of $C^*$-algebras.
