  We study non-topological and CP-violating static wall solutions in the
framework of the Minimal Supersymmetric Standard Model. We show that such
membranes, characterized by a non-trivial winding of the relative $U(1)$ phase
of the two Higgs fields in the direction orthogonal to the wall, exist for
small values of the mass of the CP-odd Higgs boson when loop corrections to the
Higgs potential are included. Although their present-day existence is excluded
by experimental bounds, we argue why they may have existed in the early
universe with important cosmological consequences.
