An n-D pure regular cell complex K is weakly well-composed (wWC) if, for each vertex v of K, the set of n-cells incident to v is face-connected. In previous work we proved that if an n-D picture I is digitally well composed (DWC) then the cubical complex Q(I) associated to I is wWC. If I is not DWC, we proposed a combinatorial algorithm to locally repair Q(I) obtaining an n-D pure simplicial complex P_S(I) homotopy equivalent to Q(I) which is always wWC. In this paper we give a combinatorial procedure to compute a simplicial complex P_S(\barI) which decomposes the complement space of |P_S(I)| and prove that P_S(\barI) is also wWC. This paper means one more step on the way to our ultimate goal: to prove that the n-D repaired complex is continuously well-composed (CWC), that is, the boundary of its continuous analog is an (n-1)-manifold.