  Non-supersymmetric multi-wall configurations are generically unstable. It is
proposed that the stabilization in compact space can be achieved by introducing
a winding number into the model. A BPS-like bound is studied for the energy of
configuration with nonvanishing winding number. Winding number is implemented
in an ${\cal N}=1$ supersymmetric nonlinear sigma model with two chiral scalar
fields and a bound states of BPS and anti-BPS walls is found to exist in
noncompact spaces. Even in compactified space $S^1$, this nontrivial bound
state persists above a critical radius of the compact dimension.
