diff --git a/Minkowski_sum_2/include/CGAL/Minkowski_sum_2/Minkowski_sum_conv_2.h b/Minkowski_sum_2/include/CGAL/Minkowski_sum_2/Minkowski_sum_conv_2.h
index 7b1bd67d5d0..b3e1a394469 100644
--- a/Minkowski_sum_2/include/CGAL/Minkowski_sum_2/Minkowski_sum_conv_2.h
+++ b/Minkowski_sum_2/include/CGAL/Minkowski_sum_2/Minkowski_sum_conv_2.h
@@ -533,7 +533,7 @@ class Minkowski_sum_by_convolution_2 {
     // list for subsequences sharing a common move_on indicator. When we
     // encounter such a subsequence that equals the size of the corresponding
     // polygon, we can safely remove it from the convolution cycle.
-    typename std::list<Labeled_segment_2>::iterator  first, curr;
+    typename std::list<Labeled_segment_2>::iterator  first, curr, newins;
     bool move_on;
     unsigned int count = 1;
     bool reduced_cycle = false;
@@ -611,7 +611,7 @@ class Minkowski_sum_by_convolution_2 {
         res = f_compare_xy(curr_pt, next_pt);
 
         if (res != EQUAL) {
-          cycle.insert(curr,
+          newins = cycle.insert(curr,
                        Labeled_segment_2(Segment_2(curr_pt, next_pt),
                                          X_curve_label((res == SMALLER),
                                                        cycle_id,
@@ -621,7 +621,13 @@ class Minkowski_sum_by_convolution_2 {
 
         cycle.erase(curr);
         cycle.erase(next);
-        curr = after_next;
+        if (res != EQUAL) {
+          //continue comparing the new combined line with the next line
+          curr = newins;
+        }
+        else {
+          curr = after_next;
+        }
 
         if (after_next != cycle.end()) {
           next = curr;