  We show that if a baryon asymmetry of the universe is generated through the
out-of-equilibrium decays of heavy scalar bilinears coupling to two fermions of
the minimal standard model, it is necessarily an asymmetry conserving $(B-L)$
which cannot survive past the electroweak phase transition because of
sphalerons. We then show that a surviving $(B-L)$ asymmetry may be generated if
the heavy scalars decay into two fermions, \underline {and into two light
scalars} (which may be detectable at hadron colliders). We list all possible
such trilinear scalar interactions, and discuss how our new baryogenesis
scenario may occur naturally in supersymmetric grand unified theories.
