diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/tangential_relaxation.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/tangential_relaxation.h
index 24d278dfc48..2c67b83005f 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/tangential_relaxation.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/tangential_relaxation.h
@@ -188,6 +188,10 @@ void tangential_relaxation(const VertexRange& vertices,
       }
       prev = n;
     }
+
+    if (first_run)
+      return true; //vertex incident only to degenerate faces
+
     if (!get(ecm, edge(first_h, tm)))
       if (to_double(first * prev) <= 0)
         return false;