diff --git a/Lib/test/test_urllib.py b/Lib/test/test_urllib.py
index 5a6dd65..f6b48cb 100644
--- a/Lib/test/test_urllib.py
+++ b/Lib/test/test_urllib.py
@@ -160,6 +160,9 @@
         for line in self.returned_obj:
             self.assertEqual(line, self.text)
 
+    def test_relativelocalfile(self):
+        self.assertRaises(ValueError,urllib.request.urlopen,'./' + self.pathname)
+
 class ProxyTests(unittest.TestCase):
 
     def setUp(self):
diff --git a/Lib/test/test_urllib2net.py b/Lib/test/test_urllib2net.py
index 54f4e0c..5fcb4cb 100644
--- a/Lib/test/test_urllib2net.py
+++ b/Lib/test/test_urllib2net.py
@@ -125,6 +125,8 @@
         finally:
             os.remove(TESTFN)
 
+        self.assertRaises(ValueError, urllib.request.urlopen,'./relative_path/to/file')
+
     # XXX Following test depends on machine configurations that are internal
     # to CNRI.  Need to set up a public server with the right authentication
     # configuration for test purposes.