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 9cdb76ac76b..fea3be49dc8 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
@@ -1025,6 +1025,9 @@ namespace internal {
       // property map of constrained vertices for relaxation
       auto vertex_constraint = [&](const vertex_descriptor v)
       {
+        if (is_constrained(v))
+          return true;
+
         for (halfedge_descriptor h : halfedges_around_target(v, mesh_))
         {
           Halfedge_status s = status(h);