  The electroweak phase transition in a constant hypermagnetic field=A0 is
studied in the Standard Model. The symmetry behaviour is investigated within
the consistent effective potential of the scalar and magnetic fields at finite
temperature. It includes the one-loop and ring diagram contributions. All
fundamental fermions and bosons are taken into consideration with their actual
masses. The only free parameter is the Higgs boson mass which is chosen to be
in the energy interval 75 GeV $\le m_H \le$=A0 115 GeV.=A0 It is found that for
the field strengths $H \sim 10^{22}- 10^{23}$G the electroweak phase transition
is of first order but a baryogenesis condition is not satisfied. For stronger
fields it=A0 becomes of second order. Hence it is concluded that the smooth
hypermagnetic field does not generate the strong first order phase transition
and the baryogenesis does not survive in the Standard Model. The comparison
with the results of other approaches is done.
