diff --git a/Lib/pickle.py b/Lib/pickle.py
index d62f014..386ffba 100644
--- a/Lib/pickle.py
+++ b/Lib/pickle.py
@@ -728,9 +728,18 @@
 
         self.memoize(obj)
 
+    def save_type(self, obj):
+        if obj is type(None):
+            return self.save_reduce(type, (None,), obj=obj)
+        elif obj is type(NotImplemented):
+            return self.save_reduce(type, (NotImplemented,), obj=obj)
+        elif obj is type(...):
+            return self.save_reduce(type, (...,), obj=obj)
+        return self.save_global(obj)
+
     dispatch[FunctionType] = save_global
     dispatch[BuiltinFunctionType] = save_global
-    dispatch[type] = save_global
+    dispatch[type] = save_type
 
 # Pickling helpers
 
diff --git a/Lib/test/pickletester.py b/Lib/test/pickletester.py
index 86869e1..86d668e 100644
--- a/Lib/test/pickletester.py
+++ b/Lib/test/pickletester.py
@@ -768,6 +768,15 @@
             u = self.loads(s)
             self.assertEqual(NotImplemented, u)
 
+    def test_singleton_types(self):
+        # Issue #6477: Test that types of built-in singletons can be pickled.
+        singletons = [None, ..., NotImplemented]
+        for singleton in singletons:
+            for proto in protocols:
+                s = self.dumps(type(singleton), proto)
+                u = self.loads(s)
+                self.assertIs(type(singleton), u)
+
     # Tests for protocol 2
 
     def test_proto(self):