diff --git a/include/Topology/map/map2.h b/include/Topology/map/map2.h
index 5906379c15dd739f43cfd1bc7be3f09760251728..82c877bfff443af3c5fdf3ff2bcd04b68d937562 100644
--- a/include/Topology/map/map2.h
+++ b/include/Topology/map/map2.h
@@ -95,6 +95,14 @@ protected:
 	 */
 	void phi2unsew(Dart d);
 
+
+	//! merge a face that has been tag as boundary with existing boundary if needed
+	/*  @param d a dart of the face
+	 */
+	void mergeFacewithBoundary(Dart d);
+
+
+
 	/*! @name Generator and Deletor
 	 *  To generate or delete faces in a 2-map
 	 *************************************************************************/
diff --git a/include/Topology/map/map2.hpp b/include/Topology/map/map2.hpp
index 6ec61a88122cdde0ec45f94eba897541a4359371..a5e5cc8cde31a1d1df0643f4ccf9a4caea441258 100644
--- a/include/Topology/map/map2.hpp
+++ b/include/Topology/map/map2.hpp
@@ -96,57 +96,55 @@ inline Dart Map2::alpha0(Dart d)
 	return phi2(d) ;
 }
 
-#ifdef NO_BOUND_MAP
+
 inline Dart Map2::alpha1(Dart d)
 {
 	return phi2(phi_1(d)) ;
 }
-#else
-// alpha1 avec bord
-inline Dart Map2::alpha1(Dart d)
-{
-	Dart e = phi_1(d);
-	Dart f = phi2(e);
 
-	if (f != e)
-		return f;
+// alpha1 avec bord: bye bye
+//inline Dart Map2::alpha1(Dart d)
+//{
+//	Dart e = phi_1(d);
+//	Dart f = phi2(e);
+//
+//	if (f != e)
+//		return f;
+//
+//	f = d;
+//	e = phi2(f);
+//	while (e != f)
+//	{
+//		f = phi1(e);
+//		e = phi2(f);
+//	}
+//	return f;
+//}
 
-	f = d;
-	e = phi2(f);
-	while (e != f)
-	{
-		f = phi1(e);
-		e = phi2(f);
-	}
-	return f;
-}
-#endif
 
-#ifdef NO_BOUND_MAP
 inline Dart Map2::alpha_1(Dart d)
 {
 	return phi1(phi2(d)) ;
 }
 
-#else
-// alpha_1 avec bord
-inline Dart Map2::alpha_1(Dart d)
-{
-	Dart e = phi2(d);
-
-	if (e != d)
-		return phi1(e);
+// alpha_1 avec bord : bye bye !!
+//inline Dart Map2::alpha_1(Dart d)
+//{
+//	Dart e = phi2(d);
+//
+//	if (e != d)
+//		return phi1(e);
+//
+//	e = d;
+//	Dart f = phi_1(d);
+//	while (phi2(f) != f)
+//	{
+//		e = phi2(f);
+//		f = phi_1(e);
+//	}
+//	return e;
+//}
 
-	e = d;
-	Dart f = phi_1(d);
-	while (phi2(f) != f)
-	{
-		e = phi2(f);
-		f = phi_1(e);
-	}
-	return e;
-}
-#endif
 
 inline void Map2::phi2sew(Dart d, Dart e)
 {
diff --git a/src/Topology/map/map2.cpp b/src/Topology/map/map2.cpp
index 6775d58cd5c7440db9d0c5394a9b8fe2b9b85f2a..601edb088a7a2633ef5bcbe07e6a336dd724e722 100644
--- a/src/Topology/map/map2.cpp
+++ b/src/Topology/map/map2.cpp
@@ -31,15 +31,34 @@ namespace CGoGN
  *  To generate or delete faces in a 2-map
  *************************************************************************/
 
-void Map2::deleteOrientedFace(Dart d)
+void Map2::mergeFacewithBoundary(Dart d)
 {
 	Dart e = d ;
-	do
+	do									// foreach edge of face
 	{
-		phi2unsew(e) ;		// unsew the face of d
-		e = phi1(e) ;		// from all its adjacent faces
+		Dart f = phi2(e);
+		if (isBoundaryMarked(f))		// if sewed to boundary
+		{
+			phi2unsew(e);// ?? not necessary
+			Dart ff = phi_1(f);
+			if (e != ff)
+				phi1sew(e, ff) ;		//    merge with it
+			Dart ee = phi_1(e);
+			if (f != ee)
+				phi1sew(f, ee) ;
+			deleteOrientedFace(e) ;
+		}
+		e = phi1(e) ;
 	} while (e != d) ;
-	Map1::deleteOrientedFace(d);	// delete the face
+}
+
+
+void Map2::deleteOrientedFace(Dart d)
+{
+	// tag face in boundary
+	boundaryMarkOrbit(FACE,d);
+	mergeFacewithBoundary(d);
+
 }
 
 /*! @name Topological Operators