diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Isotropic_remeshing/remesh_impl.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Isotropic_remeshing/remesh_impl.h
index ce6d22ab46a..705ba2adc58 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Isotropic_remeshing/remesh_impl.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Isotropic_remeshing/remesh_impl.h
@@ -48,6 +48,7 @@
 #include <boost/unordered_map.hpp>
 #include <boost/unordered_set.hpp>
 #include <boost/shared_ptr.hpp>
+#include <boost/container/flat_set.hpp>
 
 #include <map>
 #include <list>
@@ -303,6 +304,8 @@ namespace internal {
     {
       tag_halfedges_status(face_range); //called first
 
+      constrain_patch_corners(face_range);
+
       BOOST_FOREACH(face_descriptor f, face_range)
       {
         input_triangles_.push_back(triangle(f));
@@ -1372,6 +1375,43 @@ private:
         return PMP::compute_face_normal(f, mesh_);
     }
 
+    template <typename FaceRange>
+    void constrain_patch_corners(const FaceRange& face_range)
+    {
+      boost::container::flat_set<vertex_descriptor> visited;
+
+      BOOST_FOREACH(face_descriptor f, face_range)
+      {
+        BOOST_FOREACH(halfedge_descriptor h,
+                      halfedges_around_face(halfedge(f, mesh_), mesh_))
+        {
+          vertex_descriptor vt = target(h, mesh_);
+          //treat target(h, mesh_)
+          if (visited.find(vt) != visited.end())
+            continue;//already treated
+
+          if (status(h) == PATCH)//h not on patch boundary
+            continue;            //so neither is target(h, mesh_)
+
+          //count incident MESH_BORDER edges
+          unsigned int nb_incident_borders = 0;
+          BOOST_FOREACH(halfedge_descriptor hv,
+                        halfedges_around_target(h, mesh_))
+          {
+            CGAL_assertion(vt == target(hv, mesh_));
+            if ( (status(hv) == PATCH_BORDER && status(opposite(hv, mesh_)) == MESH_BORDER)
+              || (status(hv) == MESH_BORDER && status(opposite(hv, mesh_)) == PATCH_BORDER))
+            nb_incident_borders++;
+          }
+
+          if (nb_incident_borders == 1) //this is a special corner
+            set_constrained(vt, true);
+
+          visited.insert(vt);
+        }
+      }
+    }
+
     template<typename FaceRange>
     void tag_halfedges_status(const FaceRange& face_range)
     {