diff --git a/Lib/test/test_ntpath.py b/Lib/test/test_ntpath.py
index ade0790..83d794d 100644
--- a/Lib/test/test_ntpath.py
+++ b/Lib/test/test_ntpath.py
@@ -123,6 +123,11 @@
         tester("ntpath.normpath('C:////a/b')", r'C:\a\b')
         tester("ntpath.normpath('//machine/share//a/b')", r'\\machine\share\a\b')
 
+        # Issue 5827: Make sure normpath preserves unicode
+        for path in (u'', u'.', u'/', u'\\', u'///foo/.//bar//'):
+            self.assertTrue(isinstance(ntpath.normpath(path), unicode),
+                            'normpath() returned str instead of unicode')
+
     def test_expandvars(self):
         with test_support.EnvironmentVarGuard() as env:
             env.clear()
diff --git a/Lib/test/test_posixpath.py b/Lib/test/test_posixpath.py
index 3e8ffa9..0c54d83 100644
--- a/Lib/test/test_posixpath.py
+++ b/Lib/test/test_posixpath.py
@@ -381,6 +381,11 @@
         self.assertEqual(posixpath.normpath("///foo/.//bar//.//..//.//baz"), "/foo/baz")
         self.assertEqual(posixpath.normpath("///..//./foo/.//bar"), "/foo/bar")
 
+        # Issue 5827: Make sure normpath preserves unicode
+        for path in (u'', u'.', u'/', u'\\', u'///foo/.//bar//'):
+            self.assertTrue(isinstance(posixpath.normpath(path), unicode),
+                            'normpath() returned str instead of unicode')
+
         self.assertRaises(TypeError, posixpath.normpath)
 
     def test_abspath(self):