  Product systems are the classifying structures for semigroups of
endomorphisms of B(H), in that two $E_0$-semigroups are cocycle conjugate iff
their product systems are isomorphic. Thus it is important to know that every
abstract product system is associated with an $E_0$-semigrouop. This was first
proved more than fifteen years ago by rather indirect methods. Recently, Skeide
has given a more direct proof. In this note we give yet another proof by an
elementary construction.
