diff --git a/src/sage/data_structures/mutable_poset.py b/src/sage/data_structures/mutable_poset.py
index 2f30ccb4535..3848d59ddf7 100644
--- a/src/sage/data_structures/mutable_poset.py
+++ b/src/sage/data_structures/mutable_poset.py
@@ -3451,6 +3451,11 @@ def map(self, function, topological=False, reverse=False):
             Since this method works inplace, it is not allowed that
             ``function`` alters the key of an element.
 
+        .. NOTE::
+
+            If ``function`` returns ``None``, then the element is
+            removed after the mapping.
+
         EXAMPLES::
 
             sage: from sage.data_structures.mutable_poset import MutablePoset as MP
@@ -3464,6 +3469,11 @@ def map(self, function, topological=False, reverse=False):
             sage: P
             poset((1, 2, 3), (1, 3, 4), (2, 1, 3), (2, 2, 4), (4, 4, 8))
 
+        TESTS::
+
+            sage: P.map(lambda e: e if e[2] != 4 else None); P
+            poset((1, 2, 3), (2, 1, 3), (4, 4, 8))
+
         .. SEEALSO::
 
             :meth:`copy`,
@@ -3471,8 +3481,13 @@ def map(self, function, topological=False, reverse=False):
         """
         shells = self.shells_topological(reverse=reverse) \
             if topological else self.shells()
+        remove = []
         for shell in shells:
             shell._element_ = function(shell._element_)
+            if shell._element_ is None:
+                remove.append(shell.key)
+        for key in remove:
+            self.remove(key)
 
 
     def mapped(self, function):