diff --git a/Lib/test/test_ntpath.py b/Lib/test/test_ntpath.py
index 8ff7075..3d18527 100644
--- a/Lib/test/test_ntpath.py
+++ b/Lib/test/test_ntpath.py
@@ -236,6 +236,7 @@
         tester('ntpath.relpath("/", "/")', '.')
         tester('ntpath.relpath("/a", "/a")', '.')
         tester('ntpath.relpath("/a/b", "/a/b")', '.')
+        tester('ntpath.relpath("c:/foo", "C:/FOO")', '.')
 
 
 def test_main():
diff --git a/Lib/test/test_posixpath.py b/Lib/test/test_posixpath.py
index 0efe3ff..6123ae2 100644
--- a/Lib/test/test_posixpath.py
+++ b/Lib/test/test_posixpath.py
@@ -602,6 +602,15 @@
                              "../"+curdir+"/a/b")
             self.assertEqual(posixpath.relpath("a", "b/c"), "../../a")
             self.assertEqual(posixpath.relpath("a", "a"), ".")
+            self.assertEqual(posixpath.relpath("/foo/bar/bat", "/x/y/z"), '../../../foo/bar/bat')
+            self.assertEqual(posixpath.relpath("/foo/bar/bat", "/foo/bar"), 'bat')
+            self.assertEqual(posixpath.relpath("/foo/bar/bat", "/"), 'foo/bar/bat')
+            self.assertEqual(posixpath.relpath("/", "/foo/bar/bat"), '../../..')
+            self.assertEqual(posixpath.relpath("/foo/bar/bat", "/x"), '../foo/bar/bat')
+            self.assertEqual(posixpath.relpath("/x", "/foo/bar/bat"), '../../../x')
+            self.assertEqual(posixpath.relpath("/", "/"), '.')
+            self.assertEqual(posixpath.relpath("/a", "/a"), '.')
+            self.assertEqual(posixpath.relpath("/a/b", "/a/b"), '.')
         finally:
             os.getcwd = real_getcwd
 
@@ -620,6 +629,15 @@
                              b"../"+curdir+b"/a/b")
             self.assertEqual(posixpath.relpath(b"a", b"b/c"), b"../../a")
             self.assertEqual(posixpath.relpath(b"a", b"a"), b".")
+            self.assertEqual(posixpath.relpath(b"/foo/bar/bat", b"/x/y/z"), b'../../../foo/bar/bat')
+            self.assertEqual(posixpath.relpath(b"/foo/bar/bat", b"/foo/bar"), b'bat')
+            self.assertEqual(posixpath.relpath(b"/foo/bar/bat", b"/"), b'foo/bar/bat')
+            self.assertEqual(posixpath.relpath(b"/", b"/foo/bar/bat"), b'../../..')
+            self.assertEqual(posixpath.relpath(b"/foo/bar/bat", b"/x"), b'../foo/bar/bat')
+            self.assertEqual(posixpath.relpath(b"/x", b"/foo/bar/bat"), b'../../../x')
+            self.assertEqual(posixpath.relpath(b"/", b"/"), b'.')
+            self.assertEqual(posixpath.relpath(b"/a", b"/a"), b'.')
+            self.assertEqual(posixpath.relpath(b"/a/b", b"/a/b"), b'.')
 
             self.assertRaises(TypeError, posixpath.relpath, b"bytes", "str")
             self.assertRaises(TypeError, posixpath.relpath, "str", b"bytes")