diff --git a/src/sage/manifolds/differentiable/manifold.py b/src/sage/manifolds/differentiable/manifold.py
index b0ad7fdb88b..b32c1207933 100644
--- a/src/sage/manifolds/differentiable/manifold.py
+++ b/src/sage/manifolds/differentiable/manifold.py
@@ -952,7 +952,7 @@ def diff_map(self, codomain, coord_functions=None, chart1=None,
             coord_functions = {(chart1, chart2): coord_functions}
         return homset(coord_functions, name=name, latex_name=latex_name)
 
-    def diffeomorphism(self, codomain, coord_functions=None, chart1=None,
+    def diffeomorphism(self, codomain=None, coord_functions=None, chart1=None,
                        chart2=None, name=None, latex_name=None):
         r"""
         Define a diffeomorphism between the current manifold and another one.
@@ -962,8 +962,8 @@ def diffeomorphism(self, codomain, coord_functions=None, chart1=None,
 
         INPUT:
 
-        - ``codomain`` -- codomain of the diffeomorphism (the arrival manifold
-          or some subset of it)
+        - ``codomain`` -- (default: ``None``) codomain of the diffeomorphism (the arrival manifold
+          or some subset of it). If ``None``, the current manifold is taken.
         - ``coord_functions`` -- (default: ``None``) if not ``None``, must be
           either
 
@@ -1030,6 +1030,9 @@ def diffeomorphism(self, codomain, coord_functions=None, chart1=None,
         examples.
 
         """
+        if codomain is None:
+            codomain = self
+
         homset = Hom(self, codomain)
         if coord_functions is None:
             coord_functions = {}