  We discuss some results concerning the multiplication of non-commutative
random variables that are c-free with respect to a pair $( \Phi, \varphi) $,
where $ \Phi $ is a linear map with values in some Banach or C$^\ast$-algebra
and $ \varphi $ is scalar-valued. In particular, we construct a suitable
analogue of the Voiculescu's $ S $-transform for this framework.
