Thanks for the patch, I tried it on Linux and it seems to solve the problem.

A few comments about it:
1) I'd change all the self.assertEqual(type(posixpath.normpath(u"")),
unicode) to self.assertTrue(isinstance(posixpath.normpath(u""), unicode));
2) a test for normpath(u'.') should probably be added;
3) in ntpath.py the 'slash' is actually a backslash, so the name of the
var should be changed;