diff --git a/Cartesian_kernel/include/CGAL/Cartesian/Sphere_3.h b/Cartesian_kernel/include/CGAL/Cartesian/Sphere_3.h
index 824893c0cc3..4ba4266e1ff 100644
--- a/Cartesian_kernel/include/CGAL/Cartesian/Sphere_3.h
+++ b/Cartesian_kernel/include/CGAL/Cartesian/Sphere_3.h
@@ -122,7 +122,7 @@ public:
   Sphere_3 orthogonal_transform(const Aff_transformation_3 &t) const
   {
     // FIXME: precond: t.is_orthogonal() (*UNDEFINED*)
-    Vector_3 vec(FT(1), FT(0));               // unit vector
+    Vector_3 vec(FT(1), FT(0), FT(0));        // unit vector
     vec = vec.transform(t);                   // transformed
     FT sq_scale = vec.squared_length();       // squared scaling factor
 
diff --git a/Homogeneous_kernel/include/CGAL/Homogeneous/SphereH3.h b/Homogeneous_kernel/include/CGAL/Homogeneous/SphereH3.h
index 18390528295..497e10b695b 100644
--- a/Homogeneous_kernel/include/CGAL/Homogeneous/SphereH3.h
+++ b/Homogeneous_kernel/include/CGAL/Homogeneous/SphereH3.h
@@ -254,6 +254,30 @@ SphereH3<R>::bbox() const
 		maxx.sup(), maxy.sup(), maxz.sup());
 }
 
+template <class R>
+SphereH3<R>
+SphereH3<R>::
+orthogonal_transform(const typename SphereH3<R>::Aff_transformation_3& t) const
+{
+  typename R::Vector_3 vec( RT(1), RT(0), RT(0) );   // unit vector
+  vec = vec.transform(t);                     // transformed
+  FT  sq_scale = FT( vec*vec );               // squared scaling factor
+
+  if ( t.is_even() )
+  {
+      return SphereH3<R>(t.transform(center() ),
+                             sq_scale * squared_radius(),
+                             orientation() );
+  }
+  else
+  {
+      return SphereH3<R>(t.transform(center() ),
+                             sq_scale * squared_radius(),
+                             CGAL::opposite( orientation()) );
+  }
+}
+
+
 #ifndef CGAL_NO_OSTREAM_INSERT_SPHEREH3
 template < class R >
 CGAL_KERNEL_INLINE
diff --git a/Kernel_23/test/Kernel_23/include/CGAL/_test_cls_aff_transformation_3.h b/Kernel_23/test/Kernel_23/include/CGAL/_test_cls_aff_transformation_3.h
index c0d05587236..7d7b0a38202 100644
--- a/Kernel_23/test/Kernel_23/include/CGAL/_test_cls_aff_transformation_3.h
+++ b/Kernel_23/test/Kernel_23/include/CGAL/_test_cls_aff_transformation_3.h
@@ -85,6 +85,7 @@ _test_cls_aff_transformation_3(const R& )
  CGAL::Triangle_3<R>     ttri;
  CGAL::Tetrahedron_3<R>  tet(p1, p2, p3, p4);
  CGAL::Tetrahedron_3<R>  ttet;
+ CGAL::Sphere_3<R>       unit_sphere(CGAL::ORIGIN, 1);
 
 
  CGAL::Aff_transformation_3<R> ident( CGAL::IDENTITY );
@@ -536,6 +537,10 @@ _test_cls_aff_transformation_3(const R& )
  assert( scale11.homogeneous(0,0) == scale11.hm(0,0) );
  assert( translate.homogeneous(1,2) == translate.hm(1,2) );
 
+ // orthogonal_transform
+ assert (unit_sphere.orthogonal_transform(ident) == unit_sphere);
+ assert (unit_sphere.orthogonal_transform(translate).center() == pnt);
+
  std::cout << "done" << std::endl;
  return true;
 }