diff --git a/Combinatorial_map/test/Combinatorial_map/CMakeLists.txt b/Combinatorial_map/test/Combinatorial_map/CMakeLists.txt
index 271451857f9..885b68f5b53 100644
--- a/Combinatorial_map/test/Combinatorial_map/CMakeLists.txt
+++ b/Combinatorial_map/test/Combinatorial_map/CMakeLists.txt
@@ -12,6 +12,8 @@ set(hfiles Combinatorial_map_2_test.h Combinatorial_map_3_test.h
 # create a target per cppfile
 create_single_source_cgal_program(Combinatorial_map_test.cpp ${hfiles})
 create_single_source_cgal_program(Combinatorial_map_copy_test.cpp ${hfiles})
+create_single_source_cgal_program(cmap_test_split_attribute.cpp)
+create_single_source_cgal_program(Combinatorial_map_empty_it_test.cpp)
 
 # Same targets, defining USE_COMPACT_CONTAINER_WITH_INDEX to test index version
 add_executable(Combinatorial_map_test_index  Combinatorial_map_test.cpp ${hfiles})
@@ -24,7 +26,9 @@ target_compile_definitions(Combinatorial_map_copy_test_index PRIVATE USE_COMPACT
 target_link_libraries(Combinatorial_map_copy_test_index PRIVATE CGAL::CGAL CGAL::Data)
 cgal_add_compilation_test(Combinatorial_map_copy_test_index)
 
-create_single_source_cgal_program(cmap_test_split_attribute.cpp)
+add_executable(Combinatorial_map_empty_it_test_index Combinatorial_map_empty_it_test.cpp)
+target_compile_definitions(Combinatorial_map_empty_it_test_index PRIVATE USE_COMPACT_CONTAINER_WITH_INDEX)
+cgal_add_compilation_test(Combinatorial_map_empty_it_test_index)
 
 # Link with OpenMesh if possible
 find_package(OpenMesh QUIET)
diff --git a/Combinatorial_map/test/Combinatorial_map/Combinatorial_map_empty_it_test.cpp b/Combinatorial_map/test/Combinatorial_map/Combinatorial_map_empty_it_test.cpp
new file mode 100644
index 00000000000..cf8270f4b95
--- /dev/null
+++ b/Combinatorial_map/test/Combinatorial_map/Combinatorial_map_empty_it_test.cpp
@@ -0,0 +1,36 @@
+#include <CGAL/Combinatorial_map.h>
+
+struct Map_3_dart_items_3: public CGAL::Generic_map_min_items
+{
+#ifdef USE_COMPACT_CONTAINER_WITH_INDEX
+  typedef CGAL::Tag_true Use_index;
+#endif
+};
+
+using Map3=CGAL::Combinatorial_map<3, Map_3_dart_items_3>;
+
+template<typename Range>
+bool test_empty_it(Range& r, const std::string& txt)
+{
+  bool res=true;
+  Map3 m;
+  if(r.size()!=0)
+  {
+    std::cout<<"[ERROR "<<txt<<"] non zero size with range: "<<r.size()<<std::endl;
+    res=false;
+  }
+  std::size_t nb=0;
+  for(auto it=r.begin(), itend=r.end(); it!=itend; ++it)
+  { ++nb; }
+  if(nb!=0)
+  {
+    std::cout<<"[ERROR "<<txt<<"] non zero size with it: "<<nb<<std::endl;
+    res=false;
+  }
+
+  return res;
+}
+int main()
+{
+
+}