  A regularized model of the double compactified D=11 supermembrane with
nontrivial winding in terms of SU(N) valued maps is obtained. The condition of
nontrivial winding is described in terms of a nontrivial line bundle introduced
in the formulation of the compactified supermembrane. The multivalued
geometrical objects of the model related to the nontrivial wrapping are
described in terms of a SU(N) geometrical object which in the $ N\to \infty$
limit, converges to the symplectic connection related to the area preserving
diffeomorphisms of the recently obtained non-commutative description of the
compactified D=11 supermembrane.(I. Martin, J.Ovalle, A. Restuccia. 2000,2001)
  The SU(N) regularized canonical lagrangian is explicitly obtained. In the $
N\to \infty$ limit it converges to the lagrangian in (I.Martin, J.Ovalle,
A.Restuccia. 2000,2001) subject to the nontrivial winding condition. The
spectrum of the hamiltonian of the double compactified D=11 supermembrane is
discussed.
  Generically, it contains local string like spikes with zero energy.
  However the sector of the theory corresponding to a principle bundle
characterized by the winding number $n \neq 0$, described by the SU(N) model we
propose, is shown to have no local string-like spikes and hence the spectrum of
this sector should be discrete.
