diff --git a/Homogeneous_kernel/include/CGAL/Homogeneous/Homogeneous_base.h b/Homogeneous_kernel/include/CGAL/Homogeneous/Homogeneous_base.h
index a161939a4fd..fc372695991 100644
--- a/Homogeneous_kernel/include/CGAL/Homogeneous/Homogeneous_base.h
+++ b/Homogeneous_kernel/include/CGAL/Homogeneous/Homogeneous_base.h
@@ -61,7 +61,6 @@
 #include <CGAL/Homogeneous/distance_predicatesH2.h>
 #include <CGAL/Homogeneous/predicates_on_directionsH2.h>
 #include <CGAL/Homogeneous/predicates_on_pointsH2.h>
-#include <CGAL/Homogeneous/predicates_on_rtH2.h>
 
 #include <CGAL/Homogeneous/basic_constructionsH3.h>
 #include <CGAL/Homogeneous/distance_predicatesH3.h>
diff --git a/Homogeneous_kernel/include/CGAL/Homogeneous/function_objects.h b/Homogeneous_kernel/include/CGAL/Homogeneous/function_objects.h
index 75cd8d5c29a..6d0f8ad8aaf 100644
--- a/Homogeneous_kernel/include/CGAL/Homogeneous/function_objects.h
+++ b/Homogeneous_kernel/include/CGAL/Homogeneous/function_objects.h
@@ -27,6 +27,7 @@
 #include <CGAL/Kernel/function_objects.h>
 #include <CGAL/Cartesian/function_objects.h>
 #include <CGAL/Kernel/Return_base_tag.h>
+#include <CGAL/predicates/sign_of_determinant.h>
 
 CGAL_BEGIN_NAMESPACE
 
@@ -3648,21 +3649,21 @@ namespace HomogeneousKernelFunctors {
     result_type
     operator()(const Point_3& p, const Point_3& q, const Point_3& r) const
     {
-      Orientation oxy_pqr = orientationH2(p.hx(), p.hy(), p.hw(),
-					  q.hx(), q.hy(), q.hw(),
-					  r.hx(), r.hy(), r.hw());
+      Orientation oxy_pqr = sign_of_determinant3x3(p.hx(), p.hy(), p.hw(),
+					           q.hx(), q.hy(), q.hw(),
+					           r.hx(), r.hy(), r.hw());
       if (oxy_pqr != COLLINEAR)
 	return oxy_pqr;
 
-      Orientation oyz_pqr = orientationH2(p.hy(), p.hz(), p.hw(),
-					  q.hy(), q.hz(), q.hw(),
-					  r.hy(), r.hz(), r.hw());
+      Orientation oyz_pqr = sign_of_determinant3x3(p.hy(), p.hz(), p.hw(),
+					           q.hy(), q.hz(), q.hw(),
+					           r.hy(), r.hz(), r.hw());
       if (oyz_pqr != COLLINEAR)
 	return oyz_pqr;
 
-      return orientationH2(p.hx(), p.hz(), p.hw(),
-			   q.hx(), q.hz(), q.hw(),
-			   r.hx(), r.hz(), r.hw());
+      return sign_of_determinant3x3(p.hx(), p.hz(), p.hw(),
+			            q.hx(), q.hz(), q.hw(),
+			            r.hx(), r.hz(), r.hw());
     }
 
     result_type
@@ -3681,35 +3682,26 @@ namespace HomogeneousKernelFunctors {
 
       // compute orientation of p,q,s in this plane P:
       Orientation save;
-      if ( (save = orientationH2( p.hy(), p.hz(), p.hw(),
-				  q.hy(), q.hz(), q.hw(),
-				  r.hy(), r.hz(), r.hw())) != COLLINEAR)
-	{ return
-	    static_cast<Orientation>(
-	     static_cast<int>( save)
-	     * static_cast<int>( orientationH2( p.hy(), p.hz(), p.hw(),
-						q.hy(), q.hz(), q.hw(),
-						s.hy(), s.hz(), s.hw())) );
+      if ( (save = sign_of_determinant3x3(p.hy(), p.hz(), p.hw(),
+				          q.hy(), q.hz(), q.hw(),
+				          r.hy(), r.hz(), r.hw())) != COLLINEAR)
+	{ return save * sign_of_determinant3x3(p.hy(), p.hz(), p.hw(),
+					       q.hy(), q.hz(), q.hw(),
+					       s.hy(), s.hz(), s.hw());
 	}
-      if ( (save = orientationH2( p.hx(), p.hz(), p.hw(),
-				  q.hx(), q.hz(), q.hw(),
-				  r.hx(), r.hz(), r.hw())) != COLLINEAR)
-	{ return
-	    static_cast<Orientation>(
-	     static_cast<int>( save)
-	     * static_cast<int>( orientationH2( p.hx(), p.hz(), p.hw(),
-						q.hx(), q.hz(), q.hw(),
-						s.hx(), s.hz(), s.hw())) );
+      if ( (save = sign_of_determinant3x3(p.hx(), p.hz(), p.hw(),
+				          q.hx(), q.hz(), q.hw(),
+				          r.hx(), r.hz(), r.hw())) != COLLINEAR)
+	{ return save * sign_of_determinant3x3(p.hx(), p.hz(), p.hw(),
+					       q.hx(), q.hz(), q.hw(),
+					       s.hx(), s.hz(), s.hw());
 	}
-      if ( (save = orientationH2( p.hx(), p.hy(), p.hw(),
-				  q.hx(), q.hy(), q.hw(),
-				  r.hx(), r.hy(), r.hw())) != COLLINEAR)
-	{ return
-	    static_cast<Orientation>(
-	     static_cast<int>( save)
-	     * static_cast<int>( orientationH2( p.hx(), p.hy(), p.hw(),
+      if ( (save = sign_of_determinant3x3(p.hx(), p.hy(), p.hw(),
+				          q.hx(), q.hy(), q.hw(),
+				          r.hx(), r.hy(), r.hw())) != COLLINEAR)
+	{ return save * sign_of_determinant3x3( p.hx(), p.hy(), p.hw(),
 						q.hx(), q.hy(), q.hw(),
-						s.hx(), s.hy(), s.hw())) );
+						s.hx(), s.hy(), s.hw());
 	}
       CGAL_kernel_assertion( false);
       return COLLINEAR;
diff --git a/Homogeneous_kernel/include/CGAL/Homogeneous/predicates_on_rtH2.h b/Homogeneous_kernel/include/CGAL/Homogeneous/predicates_on_rtH2.h
deleted file mode 100644
index 0f4d45993c7..00000000000
--- a/Homogeneous_kernel/include/CGAL/Homogeneous/predicates_on_rtH2.h
+++ /dev/null
@@ -1,46 +0,0 @@
-// Copyright (c) 1999  Utrecht University (The Netherlands),
-// ETH Zurich (Switzerland), Freie Universitaet Berlin (Germany),
-// INRIA Sophia-Antipolis (France), Martin-Luther-University Halle-Wittenberg
-// (Germany), Max-Planck-Institute Saarbruecken (Germany), RISC Linz (Austria),
-// and Tel-Aviv University (Israel).  All rights reserved.
-//
-// This file is part of CGAL (www.cgal.org); you can redistribute it and/or
-// modify it under the terms of the GNU Lesser General Public License as
-// published by the Free Software Foundation; version 2.1 of the License.
-// See the file LICENSE.LGPL distributed with CGAL.
-//
-// Licensees holding a valid commercial license may use this file in
-// accordance with the commercial license agreement provided with the software.
-//
-// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
-// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
-//
-// $URL$
-// $Id$
-// 
-//
-// Author(s)     : Stefan Schirra
- 
-
-#ifndef CGAL_PREDICATES_ON_RTH2_H
-#define CGAL_PREDICATES_ON_RTH2_H
-
-#include <CGAL/predicates/sign_of_determinant.h>
-
-CGAL_BEGIN_NAMESPACE
-
-template <class RT>
-inline
-Orientation
-orientationH2( const RT& phx, const RT& phy, const RT& phw,
-               const RT& qhx, const RT& qhy, const RT& qhw,
-               const RT& rhx, const RT& rhy, const RT& rhw )
-{
-  return sign_of_determinant3x3(phx,phy,phw,
-                                qhx,qhy,qhw,
-                                rhx,rhy,rhw);
-}
-
-CGAL_END_NAMESPACE
-
-#endif // CGAL_PREDICATES_ON_RTH2_H