  A commonly accepted mechanism of generating baryon asymmetry in the minimal
supersymmetric standard model (MSSM) depends on the CP violating relative phase
between the gaugino mass and the Higgsino mu term. The direct constraint on
this phase comes from the limit of electric dipole moments (EDM) of various
light fermions. To avoid such a constraint, a scheme which assumes the first
two generation sfermions are very heavy is usually evoked to suppress the
one-loop EDM contributions. We point out that under such a scheme the most
severe constraint may come from a new contribution to the electric dipole
moments of the electron, the neutron or atoms via the chargino sector at the
two-loop level. As a result, the allowed parameter space for baryogenesis in
MSSM is severely constrained, independent of masses of the first two generation
sfermions.
