diff --git a/Lib/argparse.py b/Lib/argparse.py
index 2677ef63e9e541..2fb1da59f942cf 100644
--- a/Lib/argparse.py
+++ b/Lib/argparse.py
@@ -857,7 +857,6 @@ class BooleanOptionalAction(Action):
     def __init__(self,
                  option_strings,
                  dest,
-                 const=None,
                  default=None,
                  type=None,
                  choices=None,
diff --git a/Lib/test/test_argparse.py b/Lib/test/test_argparse.py
index e82a0c39c21a8b..22cae626ccc297 100644
--- a/Lib/test/test_argparse.py
+++ b/Lib/test/test_argparse.py
@@ -700,6 +700,14 @@ class TestBooleanOptionalAction(ParserTestCase):
         ('--no-foo --foo', NS(foo=True)),
     ]
 
+    def test_const(self):
+        # See bpo-40862
+        parser = argparse.ArgumentParser()
+        with self.assertRaises(TypeError) as cm:
+            parser.add_argument('--foo', const=True, action=argparse.BooleanOptionalAction)
+
+        self.assertIn("got an unexpected keyword argument 'const'", str(cm.exception))
+
 class TestBooleanOptionalActionRequired(ParserTestCase):
     """Tests BooleanOptionalAction required"""