diff --git a/include/deal.II/fe/fe_poly.templates.h b/include/deal.II/fe/fe_poly.templates.h
index 2d0938665e84..867fa10c73d9 100644
--- a/include/deal.II/fe/fe_poly.templates.h
+++ b/include/deal.II/fe/fe_poly.templates.h
@@ -268,10 +268,9 @@ FE_Poly<PolynomialType, dim, spacedim>::fill_fe_values(
 
       for (unsigned int k = 0; k < this->dofs_per_cell; ++k)
         for (unsigned int i = 0; i < quadrature.size(); ++i)
-          for (unsigned int j = 0; j < spacedim; ++j)
-            output_data.shape_hessians[k][i] -=
-              mapping_data.jacobian_pushed_forward_grads[i][j] *
-              output_data.shape_gradients[k][i][j];
+          output_data.shape_hessians[k][i] -=
+            output_data.shape_gradients[k][i] *
+            mapping_data.jacobian_pushed_forward_grads[i];
     }
 
   if (flags & update_3rd_derivatives &&