diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/stitch_borders.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/stitch_borders.h
index d8c72e59126..a88abd0a667 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/stitch_borders.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/stitch_borders.h
@@ -413,6 +413,45 @@ void stitch_borders_impl(PM& pmesh,
     run_stitch_borders(pmesh, to_stitch, uf_vertices, uf_handles);
 }
 
+template <class PM>
+void stitch_boundary_cycle_2(PM& pmesh)
+{
+  typedef typename boost::graph_traits<PM>::halfedge_descriptor halfedge_descriptor;
+
+  std::vector<halfedge_descriptor> cycles;
+  BOOST_FOREACH(halfedge_descriptor hd, halfedges(pmesh))
+  {
+    if ( is_border(hd, pmesh) )
+    {
+      if ( hd < next(hd, pmesh) && next(next(hd, pmesh), pmesh) == hd )
+      {
+        cycles.push_back(hd);
+      }
+    }
+  }
+
+  BOOST_FOREACH(halfedge_descriptor hd, cycles)
+  {
+    halfedge_descriptor nhd = next(hd, pmesh);
+
+    //nhd and its opposite will be removed
+    //update face pointer
+    set_face(hd, face(opposite(nhd, pmesh), pmesh), pmesh);
+    set_halfedge(face(hd, pmesh), hd, pmesh);
+    //update next/prev pointers
+    halfedge_descriptor tmp = prev(opposite(nhd, pmesh), pmesh);
+    set_next(tmp, hd, pmesh);
+    tmp = next(opposite(nhd, pmesh), pmesh);
+    set_next(hd, tmp, pmesh);
+    //update vertex pointers
+    set_halfedge(source(hd, pmesh), opposite(hd, pmesh), pmesh);
+    set_halfedge(target(hd, pmesh), hd, pmesh);
+
+    // remove the extra halfedges
+    remove_edge(edge(nhd, pmesh), pmesh);
+  }
+}
+
 } //end of namespace internal
 
 
@@ -484,6 +523,7 @@ void stitch_borders(PolygonMesh& pmesh, const CGAL_PMP_NP_CLASS& np)
     internal::Less_for_halfedge<PolygonMesh, VPMap>(pmesh, vpm), vpm);
 
   stitch_borders(pmesh, hedge_pairs_to_stitch);
+  internal::stitch_boundary_cycle_2(pmesh);
 }