diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Snapping/snap.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Snapping/snap.h
index e54d86a5c71..2bf04753516 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Snapping/snap.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Snapping/snap.h
@@ -762,39 +762,13 @@ std::size_t split_edges(EdgesToSplitContainer& edges_to_split,
 
       if(first_split_face)
       {
-        if(p0p2 < 0)
-        {
+        if(p0p2 <= 0 || collinear(p0,p1,p2) || collinear(p0,p2,p3))
           do_split = false;
-        }
-        else
-        {
-          bool is_deg = collinear(p0,p1,p2) || collinear(p0,p3,p2);
-          if(is_deg)
-          {
-            if(p1p3 > 0 && !(collinear(p0,p1,p3) || collinear(p1,p2,p3)))
-              first_split_face = false;
-            else
-              do_split = false;
-          }
-        }
       }
       else
       {
-        if(p1p3 < 0)
-        {
+        if(p1p3 <= 0 || collinear(p0,p1,p3) || collinear(p1,p2,p3))
           do_split = false;
-        }
-        else
-        {
-          bool is_deg = collinear(p0,p1,p3) || collinear(p1,p2,p3);
-          if(is_deg)
-          {
-            if(p1p3 > 0 && !(collinear(p0,p1,p2) || collinear(p0,p3,p2)))
-              first_split_face = false;
-            else
-              do_split = false;
-          }
-        }
       }
 
       if(do_split && !is_source_mesh_fixed)