  The generalization of multiplicative unitary notion from compact quantum
groups to compact quantum semigroups is considered. We show why the same
construction doesn't work in this case by giving examples of C*-algebras with
non-trivial comultiplication which do not admit multiplicative unitaries. By
the use of the pentagon equation we suggest a notion of an operator which gives
comultiplication on any C*-algebra. The multiplicative unitary turns out to be
its special case. We prove for some compact quantum semigroups that the
comultiplication is given by such operator.
