diff --git a/Polyline_simplification_2/examples/Polyline_simplification_2/simplify_overlapping_polyline.cpp b/Polyline_simplification_2/examples/Polyline_simplification_2/simplify_overlapping_polyline.cpp
index 2df47f53932..96fa16269a3 100644
--- a/Polyline_simplification_2/examples/Polyline_simplification_2/simplify_overlapping_polyline.cpp
+++ b/Polyline_simplification_2/examples/Polyline_simplification_2/simplify_overlapping_polyline.cpp
@@ -27,7 +27,7 @@ int main()
 {
   CT ct;
 
-  std::vector<Point> P = { Point(0,1), Point(1,1), Point(2,2), Point(3,1), Point(4,1), Point(5,1) };
+  std::vector<Point> P = { Point(0,1), Point(1,1), Point(2,2), Point(3,1), Point(4,1),   Point(4,2), Point(4,1), Point(5,1) };
   std::vector<Point> Q = { Point(5,0), Point(4,1), Point(3,1), Point(2,2), Point(1,1), Point(0,0) };
   std::vector<Point> R = { Point(3,1), Point(4,1) };
 
diff --git a/Polyline_simplification_2/include/CGAL/Polyline_simplification_2/simplify.h b/Polyline_simplification_2/include/CGAL/Polyline_simplification_2/simplify.h
index 579bcfc9707..1b40efc3202 100644
--- a/Polyline_simplification_2/include/CGAL/Polyline_simplification_2/simplify.h
+++ b/Polyline_simplification_2/include/CGAL/Polyline_simplification_2/simplify.h
@@ -155,9 +155,15 @@ public:
     Constraint_iterator cit = pct.constraints_begin(), e = pct.constraints_end();
     for(; cit!=e; ++cit){
       Constraint_id cid = *cit;
-      Vertices_in_constraint_iterator it = pct.vertices_in_constraint_begin(cid);
+      Vertices_in_constraint_iterator it = pct.vertices_in_constraint_begin(cid),
+                                      ite = pct.vertices_in_constraint_end(cid);
       (*it)->set_removable(false);
-      it = pct.vertices_in_constraint_end(cid);
+      ++it;
+      for(; it != ite; ++it){
+        if((boost::next(it) != ite) && (boost::prior(it)== boost::next(it))){
+          (*it)->set_removable(false);
+        }
+      }
       it = boost::prior(it);
       (*it)->set_removable(false);
     }