diff --git a/BGL/include/CGAL/boost/graph/Euler_operations.h b/BGL/include/CGAL/boost/graph/Euler_operations.h
index f8c79165bc5..f788ec18113 100644
--- a/BGL/include/CGAL/boost/graph/Euler_operations.h
+++ b/BGL/include/CGAL/boost/graph/Euler_operations.h
@@ -1575,9 +1575,8 @@ collapse_edge(typename boost::graph_traits<Graph>::edge_descriptor e,
   bool lBottomFaceExists      = ! is_border(qp,g);
   bool lTopLeftFaceExists     = lTopFaceExists    && ! is_border(pt,g);
   bool lBottomRightFaceExists = lBottomFaceExists && ! is_border(qb,g);
-
-  CGAL_precondition( !lTopFaceExists    || (lTopFaceExists    && ( degree(target(pt, g), g) > 2 ) ) ) ;
-  CGAL_precondition( !lBottomFaceExists || (lBottomFaceExists && ( degree(target(qb, g), g) > 2 ) ) ) ;
+  bool lBottomIsTriangle       = lBottomFaceExists && next(next(qp, g), g) == prev(qp,g);
+  bool lTopIsTriangle          = lTopFaceExists && next(next(pq, g), g) == prev(pq,g);
 
   vertex_descriptor q = target(pq, g);
   vertex_descriptor p = source(pq, g);
@@ -1585,7 +1584,7 @@ collapse_edge(typename boost::graph_traits<Graph>::edge_descriptor e,
 
   bool lP_Erased = false;
 
-  if ( lTopFaceExists )
+  if ( lTopFaceExists && lTopIsTriangle)
   {
     CGAL_precondition( ! is_border(opposite(pt, g),g) ) ; // p-q-t is a face of the mesh
     if ( lTopLeftFaceExists )
@@ -1612,7 +1611,7 @@ collapse_edge(typename boost::graph_traits<Graph>::edge_descriptor e,
     }
   }
 
-  if ( lBottomFaceExists )
+  if ( lBottomFaceExists && lBottomIsTriangle)
   {
     CGAL_precondition( ! is_border(opposite(qb, g),g) ) ; // p-q-b is a face of the mesh
     if ( lBottomRightFaceExists )
diff --git a/BGL/test/BGL/data/polygon_mesh_to_collapse.off b/BGL/test/BGL/data/polygon_mesh_to_collapse.off
new file mode 100644
index 00000000000..1a25e940585
--- /dev/null
+++ b/BGL/test/BGL/data/polygon_mesh_to_collapse.off
@@ -0,0 +1,42 @@
+OFF
+25 13 0
+
+0.39160239696502686 1.3864846229553223 4.8046874923102223e-08
+0.053782559931278229 1.3864846229553223 4.8046874923102223e-08
+-0.94644606113433838 1.6651756763458252 4.8046874923102223e-08
+-1.3082554340362549 1.7385153770446777 4.8046874923102223e-08
+-1.3033660650253296 1.1860226392745972 4.8046874923102223e-08
+1.61628258228302 -0.17601536214351654 4.8046874923102223e-08
+0.55834579467773438 -0.19216139614582062 4.8046874923102223e-08
+0.053782559931278229 -0.17601536214351654 4.8046874923102223e-08
+-0.24240998923778534 -0.22679123282432556 4.8046874923102223e-08
+-0.58168435096740723 -0.25845989584922791 4.8046874923102223e-08
+-1.2915089130401611 -0.17601536214351654 4.8046874923102223e-08
+-1.50871741771698 -0.17601536214351654 4.8046874923102223e-08
+1.61628258228302 -1.7385153770446777 4.8046874923102223e-08
+1.1978726387023926 -1.7385153770446777 4.8046874923102223e-08
+0.71942150592803955 -1.7385153770446777 4.8046874923102223e-08
+0.053782559931278229 -1.7385153770446777 4.8046874923102223e-08
+-0.73973840475082397 -1.7385153770446777 4.8046874923102223e-08
+1.61628258228302 0.36264327168464661 4.8046874923102223e-08
+-0.26156377792358398 0.45463424921035767 4.8046874923102223e-08
+-0.028661971911787987 -0.78840988874435425 4.8046874923102223e-08
+0.053782559931278229 -1.2213115692138672 4.8046874923102223e-08
+-1.5918357372283936 1.5331641435623169 4.8046874923102223e-08
+-1.6162823438644409 0.87338578701019287 4.8046874923102223e-08
+-1.50871741771698 -0.0072435899637639523 4.8046874923102223e-08
+-1.50871741771698 -1.3000825643539429 4.8046874923102223e-08
+7  18 2 3 4 22 9 8
+3  2 18 1
+7  18 7 6 5 17 0 1
+7  12 5 6 7 8 19 13
+6  11 24 16 15 20 10
+3  9 19 8
+4  10 20 19 9
+3  7 18 8
+3  14 20 15
+4  13 19 20 14
+3  3 21 4
+4  9 22 23 10
+3  10 23 11
+
diff --git a/BGL/test/BGL/test_Collapse_edge.cpp b/BGL/test/BGL/test_Collapse_edge.cpp
index 69f1c347a5e..ecbaff8fe36 100644
--- a/BGL/test/BGL/test_Collapse_edge.cpp
+++ b/BGL/test/BGL/test_Collapse_edge.cpp
@@ -2,7 +2,6 @@
 
 #include <CGAL/boost/graph/Euler_operations.h>
 #include <CGAL/boost/graph/IO/OFF.h>
-
 #include <boost/range/distance.hpp>
 
 #include <string>
@@ -213,12 +212,30 @@ collapse_edge_test()
     assert(found == 2);
     CGAL::clear(test_mesh);
   }
+  // Case 6 non pure triangle mesh
+  {
+    Mesh ref;
+    if(!CGAL::IO::read_OFF("data/polygon_mesh_to_collapse.off", ref))
+    {
+      std::cout << "Error reading file: data/polygon_mesh_to_collapse.off" << std::endl;
+      exit(1);
+    }
+    std::size_t nbe=halfedges(ref).size();
+    for (std::size_t i=0; i< nbe; ++i)
+    {
+      Mesh m = ref;
+      auto h = *std::next(halfedges(m).begin(), i);
+
+      if (CGAL::Euler::does_satisfy_link_condition(edge(h,m),m))
+        CGAL::Euler::collapse_edge(edge(h,m), m);
+      assert(CGAL::is_valid_polygon_mesh(m));
+    }
+  }
 }
 
 
 int main()
 {
-
   collapse_edge_test<Polyhedron>();
   collapse_edge_test<SM>();