diff --git a/NewKernel_d/include/CGAL/NewKernel_d/orientationC5.h b/NewKernel_d/include/CGAL/NewKernel_d/orientationC5.h
index a2a927aaf26..cbe8e30c501 100644
--- a/NewKernel_d/include/CGAL/NewKernel_d/orientationC5.h
+++ b/NewKernel_d/include/CGAL/NewKernel_d/orientationC5.h
@@ -1,6 +1,3 @@
-
-
-
 typedef double RT;
 
 RT
@@ -11,36 +8,35 @@ determinant(
  RT a30,  RT a31,  RT a32,  RT a33,  RT a34,
  RT a40,  RT a41,  RT a42,  RT a43,  RT a44)
 {
-// First compute the det2x2
-  const RT m01 = a10*a01 - a00*a11;
-  const RT m02 = a20*a01 - a00*a21;
-  const RT m03 = a30*a01 - a00*a31;
-  const RT m04 = a40*a01 - a00*a41;
-  const RT m12 = a20*a11 - a10*a21;
-  const RT m13 = a30*a11 - a10*a31;
-  const RT m14 = a40*a11 - a10*a41;
-  const RT m23 = a30*a21 - a20*a31;
-  const RT m24 = a40*a21 - a20*a41;
-  const RT m34 = a40*a31 - a30*a41;
-// Now compute the minors of rank 3
-  const RT m012 = m12*a02 - m02*a12 + m01*a22;
-  const RT m013 = m13*a02 - m03*a12 + m01*a32;
-  const RT m014 = m14*a02 - m04*a12 + m01*a42;
-  const RT m023 = m23*a02 - m03*a22 + m02*a32;
-  const RT m024 = m24*a02 - m04*a22 + m02*a42;
-  const RT m034 = m34*a02 - m04*a32 + m03*a42;
-  const RT m123 = m23*a12 - m13*a22 + m12*a32;
-  const RT m124 = m24*a12 - m14*a22 + m12*a42;
-  const RT m134 = m34*a12 - m14*a32 + m13*a42;
-  const RT m234 = m34*a22 - m24*a32 + m23*a42;
-// Now compute the minors of rank 4
-  const RT m0123 = m123*a03 - m023*a13 + m013*a23 - m012*a33;
-  const RT m0124 = m124*a03 - m024*a13 + m014*a23 - m012*a43;
-  const RT m0134 = m134*a03 - m034*a13 + m014*a33 - m013*a43;
-  const RT m0234 = m234*a03 - m034*a23 + m024*a33 - m023*a43;
-  const RT m1234 = m234*a13 - m134*a23 + m124*a33 - m123*a43;
-// Now compute the minors of rank 5
-  const RT m01234 = m1234*a04 - m0234*a14 + m0134*a24 - m0124*a34 + m0123*a44;
+  RT m01 = a10*a01 - a00*a11;
+  RT m02 = a20*a01 - a00*a21;
+  RT m03 = a30*a01 - a00*a31;
+  RT m04 = a40*a01 - a00*a41;
+  RT m12 = a20*a11 - a10*a21;
+  RT m13 = a30*a11 - a10*a31;
+  RT m14 = a40*a11 - a10*a41;
+  RT m23 = a30*a21 - a20*a31;
+  RT m24 = a40*a21 - a20*a41;
+  RT m34 = a40*a31 - a30*a41;
+
+  RT m012 = m12*a02 - m02*a12 + m01*a22;
+  RT m013 = m13*a02 - m03*a12 + m01*a32;
+  RT m014 = m14*a02 - m04*a12 + m01*a42;
+  RT m023 = m23*a02 - m03*a22 + m02*a32;
+  RT m024 = m24*a02 - m04*a22 + m02*a42;
+  RT m034 = m34*a02 - m04*a32 + m03*a42;
+  RT m123 = m23*a12 - m13*a22 + m12*a32;
+  RT m124 = m24*a12 - m14*a22 + m12*a42;
+  RT m134 = m34*a12 - m14*a32 + m13*a42;
+  RT m234 = m34*a22 - m24*a32 + m23*a42;
+
+  RT m0123 = m123*a03 - m023*a13 + m013*a23 - m012*a33;
+  RT m0124 = m124*a03 - m024*a13 + m014*a23 - m012*a43;
+  RT m0134 = m134*a03 - m034*a13 + m014*a33 - m013*a43;
+  RT m0234 = m234*a03 - m034*a23 + m024*a33 - m023*a43;
+  RT m1234 = m234*a13 - m134*a23 + m124*a33 - m123*a43;
+
+  RT m01234 = m1234*a04 - m0234*a14 + m0134*a24 - m0124*a34 + m0123*a44;
   return m01234;
 }
 
@@ -53,6 +49,11 @@ orientationC5(RT p0, RT p1, RT p2, RT p3, RT p4,
               RT s0, RT s1, RT s2, RT s3, RT s4,
               RT t0, RT t1, RT t2, RT t3, RT t4,
               RT u0, RT u1, RT u2, RT u3, RT u4)
+group p0 q0 r0 s0 t0 u0;
+group p1 q1 r1 s1 t1 u1;
+group p2 q2 r2 s2 t2 u2;
+group p3 q3 r3 s3 t3 u3;
+group p4 q4 r4 s4 t4 u4;
 {
   RT pq0 = q0 - p0;
   RT pq1 = q1 - p1;
@@ -85,6 +86,5 @@ orientationC5(RT p0, RT p1, RT p2, RT p3, RT p4,
                        pt0, pt1, pt2, pt3, pt4,
                        pu0, pu1, pu2, pu3, pu4);
 
-  if (det > 0) return 1;
-  if (det < 0) return -1;
+  return sign(det);
 }