  Electroweak phase transition in a magnetic field is investigated within the
one-loop and ring diagram contributions to the effective potential in the
minimal Standard Model. All fundamental fermions and bosons are included with
their actual values of masses and the Higgs boson mass is considered in the
range $75 GeV \leq m_H \leq 115 GeV$. The effective potential is real at
sufficiently high temperature. The important role of fermions and $W$-bosons in
symmetry behaviour is observed. It is found that the phase transition for the
field strengths $10^{23} - 10^{24}$G is of first order but the baryogenesis
condition is not satisfied. The comparison with the hypermagnetic field case is
done.
