diff --git a/Lib/test/test_os.py b/Lib/test/test_os.py
index e9b0652ab0d..50b583162ed 100644
--- a/Lib/test/test_os.py
+++ b/Lib/test/test_os.py
@@ -43,6 +43,13 @@ class FileTests(unittest.TestCase):
         os.closerange(first, first + 2)
         self.assertRaises(OSError, os.write, first, "a")
 
+    def test_rename(self):
+        path = support.TESTFN
+        old = sys.getrefcount(path)
+        self.assertRaises(TypeError, os.rename, path, 0)
+        new = sys.getrefcount(path)
+        self.assertEqual(old, new)
+
 class TemporaryFileTests(unittest.TestCase):
     def setUp(self):
         self.files = []