diff --git a/Triangulation_2/include/CGAL/Polyline_constraint_hierarchy_2.h b/Triangulation_2/include/CGAL/Polyline_constraint_hierarchy_2.h
index 1f3071db44e..7731a8686ec 100644
--- a/Triangulation_2/include/CGAL/Polyline_constraint_hierarchy_2.h
+++ b/Triangulation_2/include/CGAL/Polyline_constraint_hierarchy_2.h
@@ -760,13 +760,13 @@ Polyline_constraint_hierarchy_2<T,Compare,Data>::concatenate2(Constraint_id firs
   // now we really concatenate the vertex lists
   // Note that all iterators pointing into second remain valid.
   first.vl_ptr()->pop_back(); // because it is the same as second.front()
-  Vertex_it back_it = first.vl_ptr()->skip_end();
-  --back_it;
+  Vertex_it back_it = second.vl_ptr()->skip_begin();
+
   second.vl_ptr()->splice(second.vl_ptr()->skip_begin(), *(first.vl_ptr()), first.vl_ptr()->skip_begin(), first.vl_ptr()->skip_end());
 
   // Note that for VC8 with iterator debugging the iterators pointing into second
   // are NOT valid      So we have to update them
-  for(Vertex_it it = back_it, succ = it, end = first.vl_ptr()->skip_end(); 
+  for(Vertex_it it = second.vl_ptr()->skip_begin(), succ = it, end = back_it; 
       ++succ != end; 
       ++it){
     typename Sc_to_c_map::iterator scit = sc_to_c_map.find(make_edge(*it,*succ));
diff --git a/Triangulation_2/test/Triangulation_2/issue_4025.cpp b/Triangulation_2/test/Triangulation_2/issue_4025.cpp
new file mode 100644
index 00000000000..af37b05ac06
--- /dev/null
+++ b/Triangulation_2/test/Triangulation_2/issue_4025.cpp
@@ -0,0 +1,89 @@
+#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
+#include <CGAL/Triangulation_2.h>
+#include <CGAL/Constrained_Delaunay_triangulation_2.h>
+#include <CGAL/Constrained_triangulation_plus_2.h>
+
+
+typedef CGAL::Exact_predicates_inexact_constructions_kernel                 K;
+typedef CGAL::Polygon_2<K>                                                Polygon_2;
+typedef CGAL::Exact_intersections_tag                                     Itag_;
+typedef CGAL::Constrained_Delaunay_triangulation_2<K,CGAL::Default, Itag_> CDT;
+typedef CGAL::Constrained_triangulation_plus_2<CDT>                       CDTP;
+
+typedef CDTP::Point                                                       Point;
+typedef CDTP::Constraint_id                                               Cid;
+typedef CDTP::Vertex_handle                                               Vertex_handle;
+typedef CDTP::Constraint_id                                               Constraint_id;
+typedef CDTP::Vertices_in_constraint_iterator                             Vertices_in_constraint_iterator;
+
+int countVertex(CDTP &cdtp, CDTP::Constraint_id id)
+{
+    Vertices_in_constraint_iterator v=cdtp.vertices_in_constraint_begin(id);
+
+    int count=0;
+    while(v!=cdtp.vertices_in_constraint_end(id))
+    {
+        count++;
+        v++;
+    }
+
+    return count;
+}
+
+
+int main()
+{
+    CDTP cdtp;
+
+    std::list<Point> pointsListCollinear;
+
+    pointsListCollinear.push_back(Point(0,0));
+    pointsListCollinear.push_back(Point(0,1));
+    pointsListCollinear.push_back(Point(0,2));
+    pointsListCollinear.push_back(Point(0,3));
+    pointsListCollinear.push_back(Point(0,4));
+    pointsListCollinear.push_back(Point(0,5));
+
+    std::list<Point> pointsListNoCollinear;
+
+    pointsListNoCollinear.push_back(Point(1,0));
+    pointsListNoCollinear.push_back(Point(2,1));
+    pointsListNoCollinear.push_back(Point(4,2));
+    pointsListNoCollinear.push_back(Point(2,3));
+    pointsListNoCollinear.push_back(Point(4,4));
+    pointsListNoCollinear.push_back(Point(1,5));
+
+
+    Constraint_id ctIdCollinear=cdtp.insert_constraint(pointsListCollinear.begin(),pointsListCollinear.end());
+    Constraint_id ctIdNoCollinear=cdtp.insert_constraint(pointsListNoCollinear.begin(),pointsListNoCollinear.end());
+    
+    
+    //******************************* attempt with the collinear constraint
+    Vertices_in_constraint_iterator vertexToRemoveCollinear=cdtp.vertices_in_constraint_begin(ctIdCollinear);
+    vertexToRemoveCollinear++;
+    vertexToRemoveCollinear++;
+
+
+        std::cout<<"attempt to remove vertex "<<(*vertexToRemoveCollinear)->point().x()<<" , "<<(*vertexToRemoveCollinear)->point().y() <<std::endl;
+    cdtp.remove_vertex_from_constraint(ctIdCollinear,vertexToRemoveCollinear);
+
+    std::cout<<"number of subconstraints "<<cdtp.number_of_subconstraints()<<std::endl; //--> 5, expected 4
+    std::cout<<"number of constraints "<<cdtp.number_of_constraints()<<std::endl; //--> 1
+    std::cout<<"number of vertex in constraint "<<countVertex(cdtp,ctIdCollinear)<<std::endl; //--> 6, expected 5
+    
+    
+    //******************************* attempt with the collinear constraint
+    Vertices_in_constraint_iterator vertexToRemoveNoCollinear=cdtp.vertices_in_constraint_begin(ctIdNoCollinear);
+    vertexToRemoveNoCollinear++;
+    vertexToRemoveNoCollinear++;
+
+        std::cout<<"attempt to remove vertex "<<(*vertexToRemoveNoCollinear)->point().x()<<" , "<<(*vertexToRemoveNoCollinear)->point().y() << std::endl;
+    cdtp.remove_vertex_from_constraint(ctIdNoCollinear,vertexToRemoveNoCollinear);
+
+    std::cout<<"number of subconstraints "<<cdtp.number_of_subconstraints()<<std::endl; //--> 4, ok
+    std::cout<<"number of constraints "<<cdtp.number_of_constraints()<<std::endl;  //--> 1
+    std::cout<<"number of vertex in constraint "<<countVertex(cdtp,ctIdNoCollinear)<<std::endl;  //--> 5, ok
+
+    return 0;
+
+}