diff --git a/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/GarlandHeckbert_policies.h b/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/GarlandHeckbert_policies.h
index 905f63e68b7..6a8b2bfe329 100644
--- a/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/GarlandHeckbert_policies.h
+++ b/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/GarlandHeckbert_policies.h
@@ -159,7 +159,8 @@ public:
   typedef GeomTraits                                                            Geom_traits;
   typedef typename Geom_traits::FT                                              FT;
 
-  typedef typename Eigen::Matrix<FT, 4, 4>                                      Cost_matrix;
+  typedef typename internal::GarlandHeckbert_matrix_type<TriangleMesh,
+                                                         GeomTraits>::type      Cost_matrix;
   typedef CGAL::dynamic_vertex_property_t<Cost_matrix>                          Cost_property;
   typedef typename boost::property_map<TriangleMesh, Cost_property>::type       Vertex_cost_map;
 
diff --git a/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/internal/GarlandHeckbert_core.h b/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/internal/GarlandHeckbert_core.h
index 58245e99ee1..240f9580076 100644
--- a/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/internal/GarlandHeckbert_core.h
+++ b/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/internal/GarlandHeckbert_core.h
@@ -24,6 +24,13 @@ namespace CGAL {
 namespace Surface_mesh_simplification {
 namespace internal {
 
+template<class TM_, typename GT_>
+struct GarlandHeckbert_matrix_type
+{
+  typedef typename GT_::FT                                                      FT;
+  typedef Eigen::Matrix<FT, 4, 4, Eigen::DontAlign>                             type;
+};
+
 template<class TM_, class VPM_, typename GT_>
 struct GarlandHeckbert_core
 {
@@ -43,7 +50,7 @@ struct GarlandHeckbert_core
   typedef typename Geom_traits::Plane_3                                         Plane_3;
   typedef typename Geom_traits::Vector_3                                        Vector_3;
 
-  typedef Eigen::Matrix<FT, 4, 4>                                               Matrix4x4;
+  typedef typename GarlandHeckbert_matrix_type<TM_, GT_>::type                  Matrix4x4;
   typedef Eigen::Matrix<FT, 1, 4>                                               Row4;
   typedef Eigen::Matrix<FT, 4, 1>                                               Col4;
 
@@ -170,7 +177,7 @@ struct GarlandHeckbert_core
                                          const Geom_traits& gt,
                                          const FT discontinuity_multiplier = FT(100))
   {
-    Matrix4x4 nq = Eigen::Matrix<FT, 4, 4>::Zero();
+    Matrix4x4 nq = Matrix4x4::Zero();
     for(vertex_descriptor v : vertices(tmesh))
       put(vcm, v, nq); // @todo is that necessary ?