  We study the electroweak phase transition in a supersymmetric version of the
Standard Model, in which a gauge singlet superfield is added to the Higgs
sector. We show that the order of the transition is determined by the trilinear
soft supersymmetry breaking terms rather than by the $O ( m^{3} T )$ term in
the 1-loop, $T\neq0$ corrections. This fact removes the Standard Model upper
bound on the Higgs mass, $ m_{H} < 55 GeV$, coming from the requirement that
baryon asymmetry is not washed out by anomalous electroweak processes. We
perform a numerical analysis of parameter space including in the effective
potential top-stop contribution to 1-loop radiative corrections. We find that
this model is compatible with the preservation of baryon asymmetry for masses
of the lightest scalar up to about 170 GeV.
