diff --git a/BGL/include/CGAL/boost/graph/copy_face_graph.h b/BGL/include/CGAL/boost/graph/copy_face_graph.h
index c396484f4ed..19755ac8e46 100644
--- a/BGL/include/CGAL/boost/graph/copy_face_graph.h
+++ b/BGL/include/CGAL/boost/graph/copy_face_graph.h
@@ -167,6 +167,8 @@ void copy_face_graph_impl(const SourceMesh& sm, TargetMesh& tm,
   for(tm_vertex_descriptor v : vertices(tm))
   {
     tm_halfedge_descriptor h = halfedge(v, tm);
+    if (h==boost::graph_traits<TargetMesh>::null_halfedge())
+      continue;
     tm_halfedge_descriptor next_around_vertex=h;
     do{
       next_around_vertex=opposite(next(next_around_vertex, tm), tm);
diff --git a/BGL/test/BGL/test_Euler_operations.cpp b/BGL/test/BGL/test_Euler_operations.cpp
index 0711cf379ed..6e9418c8ca8 100644
--- a/BGL/test/BGL/test_Euler_operations.cpp
+++ b/BGL/test/BGL/test_Euler_operations.cpp
@@ -35,6 +35,57 @@ test_copy_face_graph_nm_umbrella()
   }
 }
 
+template <typename T>
+void
+test_copy_face_graph_isolated_vertices()
+{
+  typedef Kernel::Point_3 Point_3;
+
+  {
+    T s, t;
+    add_vertex(s);
+    CGAL::copy_face_graph(s, t);
+  }
+
+  {
+    T s, t;
+    add_vertex(t);
+    CGAL::copy_face_graph(s, t);
+  }
+
+  {
+    T s, t;
+    CGAL::make_triangle(Point_3(), Point_3(), Point_3(), s);
+    add_vertex(s);
+    t=s;
+    CGAL::copy_face_graph(s, t);
+  }
+
+  {
+    T s, t;
+    CGAL::make_triangle(Point_3(), Point_3(), Point_3(), s);
+    add_vertex(s);
+    add_vertex(t);
+    CGAL::copy_face_graph(s, t);
+  }
+
+  {
+    T s, t;
+    CGAL::make_tetrahedron(Point_3(), Point_3(), Point_3(), Point_3(), s);
+    add_vertex(s);
+    t=s;
+    CGAL::copy_face_graph(s, t);
+  }
+
+  {
+    T s, t;
+    CGAL::make_tetrahedron(Point_3(), Point_3(), Point_3(), Point_3(), s);
+    add_vertex(s);
+    add_vertex(t);
+    CGAL::copy_face_graph(s, t);
+  }
+}
+
 template <typename T>
 void
 join_face_test()
@@ -619,6 +670,7 @@ void
 test_Euler_operations()
 {
   test_copy_face_graph_nm_umbrella<Graph>();
+  test_copy_face_graph_isolated_vertices<Graph>();
   join_face_test<Graph>();
   add_vertex_and_face_to_border_test<Graph>();
   add_face_to_border_test<Graph>();