  We will introduce the notion of strong Morita equivalence for completely
positive linear maps and study its basic properties. Also, we will discuss the
relation between strong Morita equivalence for bounded $C^*$-bimodule linear
maps and strong Morita equivalence for completely positive linear maps.
Furthermore, we will show that if two unital $C^*$-algebras are strongly Morita
equivalent, then there is a $1-1$ correspondence between the two sets of all
strong Morita equivalence classes of completely positive linear maps on the two
unital $C^*$-algebras and we will show that the corresponding two classes of
the completely positive linear maps are also strongly Morita equivalent.
