diff --git a/Cartesian_kernel/include/CGAL/Cartesian_converter.h b/Cartesian_kernel/include/CGAL/Cartesian_converter.h
index b890e3b5f77..89595b5ef34 100644
--- a/Cartesian_kernel/include/CGAL/Cartesian_converter.h
+++ b/Cartesian_kernel/include/CGAL/Cartesian_converter.h
@@ -396,24 +396,25 @@ public:
       return std::make_pair(operator()(pp.first), operator()(pp.second));
     }
 
-    typename K2::Aff_transformation_3
-    operator()(const typename K1::Aff_transformation_3 &a) const
+    typename K2::Aff_transformation_2
+    operator()(const typename K1::Aff_transformation_2& a) const
     {
-        typedef typename K2::Aff_transformation_3 Aff_transformation_3;
-      typename K2::FT t[12];
-      for(int i=0; i< 3; ++i)
-      {
-        for(int j=0; j<4; ++j)
-        {
-          t[i*4+j] = a.m(i,j);
-        }
-      }
-      return Aff_transformation_3(
-            t[0],t[1],t[2],t[3],
-            t[4],t[5],t[6],t[7],
-            t[8],t[9],t[10],t[11],
-            a.m(3,3));
+      typedef typename K2::Aff_transformation_2 Aff_transformation_2;
+      return Aff_transformation_2(c(a.m(0,0)), c(a.m(0,1)), c(a.m(0,2)),
+                                  c(a.m(1,0)), c(a.m(1,1)), c(a.m(1,2)),
+                                  c(a.m(2,2)));
     }
+
+    typename K2::Aff_transformation_3
+    operator()(const typename K1::Aff_transformation_3& a) const
+    {
+      typedef typename K2::Aff_transformation_3 Aff_transformation_3;
+      return Aff_transformation_3(c(a.m(0,0)), c(a.m(0,1)), c(a.m(0,2)), c(a.m(0,3)),
+                                  c(a.m(1,0)), c(a.m(1,1)), c(a.m(1,2)), c(a.m(1,3)),
+                                  c(a.m(2,0)), c(a.m(2,1)), c(a.m(2,2)), c(a.m(2,3)),
+                                  c(a.m(3,3)));
+    }
+
 private:
     Converter c;
     K2 k;