diff --git a/Lib/enum.py b/Lib/enum.py
index 9f9c89e..49c46ea 100644
--- a/Lib/enum.py
+++ b/Lib/enum.py
@@ -823,7 +823,7 @@ def _find_data_type(bases):
                         data_types.add(candidate or base)
                         break
                     else:
-                        candidate = base
+                        candidate = candidate or base
             if len(data_types) > 1:
                 raise TypeError('%r: too many data types: %r' % (class_name, data_types))
             elif data_types:
diff --git a/Lib/test/test_enum.py b/Lib/test/test_enum.py
index ceb0da8..956b834 100644
--- a/Lib/test/test_enum.py
+++ b/Lib/test/test_enum.py
@@ -658,6 +658,14 @@ class MyEnum(HexInt, enum.Enum):
             def __repr__(self):
                 return '<%s.%s: %r>' % (self.__class__.__name__, self._name_, self._value_)
         self.assertEqual(repr(MyEnum.A), '<MyEnum.A: 0x1>')
+        #
+        class SillyInt(HexInt):
+            pass
+        class MyOtherEnum(SillyInt, enum.Enum):
+            D = 4
+            E = 5
+            F = 6
+        self.assertIs(MyOtherEnum._member_type_, SillyInt)
 
     def test_too_many_data_types(self):
         with self.assertRaisesRegex(TypeError, 'too many data types'):