diff --git a/Arrangement_on_surface_2/include/CGAL/Arr_polyline_traits_2.h b/Arrangement_on_surface_2/include/CGAL/Arr_polyline_traits_2.h
index 8ec4e4663f4..9fff9931512 100644
--- a/Arrangement_on_surface_2/include/CGAL/Arr_polyline_traits_2.h
+++ b/Arrangement_on_surface_2/include/CGAL/Arr_polyline_traits_2.h
@@ -1033,7 +1033,8 @@ public:
         if (i1 == INVALID_INDEX) return oi;
 
         if (equal(max_vertex(cv1[i1]), min_vertex(cv2[i2]))) {
-          if ((i1 == n1-1) || (i1 == 0)){
+          if (((dir1 == SMALLER) && (i1 == n1-1)) ||
+              ((dir1 == LARGER) && (i1 == 0))){
             // cv1's right endpoint equals cv2's left endpoint
             // Thus we can return this single(!) intersection point
             std::pair<Point_2,Multiplicity>  p(max_vertex(cv1[i1]), 0);
@@ -1052,7 +1053,8 @@ public:
         if (i2 == INVALID_INDEX) return oi;
 
         if (equal(max_vertex(cv2[i2]), min_vertex(cv1[i1]))) {
-          if ((i2 == n2-1) || (i2 == 0)){
+          if (((dir2 == SMALLER) && (i2 == n2-1)) ||
+              ((dir2 == LARGER) && (i2 == 0))){
             // cv2's right endpoint equals cv1's left endpoint
             // Thus we can return this single(!) intersection point
             std::pair<Point_2,Multiplicity>  p(max_vertex(cv2[i2]), 0);
@@ -1061,7 +1063,6 @@ public:
           }
 
           dir2 == SMALLER ? ++i2 : --i2;
-          std::cout << "i2 = " << i2 << "\n";
           left_res = EQUAL;
         }
       }