diff --git a/Lib/ntpath.py b/Lib/ntpath.py
index 11a0a3e..091a242 100644
--- a/Lib/ntpath.py
+++ b/Lib/ntpath.py
@@ -488,8 +488,8 @@
 
     if not path:
         raise ValueError("no path specified")
-    start_list = abspath(start).split(sep)
-    path_list = abspath(path).split(sep)
+    start_list = [x for x in abspath(start).split(sep) if x]
+    path_list = [x for x in abspath(path).split(sep) if x]
     if start_list[0].lower() != path_list[0].lower():
         unc_path, rest = splitunc(path)
         unc_start, rest = splitunc(start)
diff --git a/Lib/posixpath.py b/Lib/posixpath.py
index 81f25b8..aae38d5 100644
--- a/Lib/posixpath.py
+++ b/Lib/posixpath.py
@@ -403,8 +403,8 @@
     if not path:
         raise ValueError("no path specified")
 
-    start_list = abspath(start).split(sep)
-    path_list = abspath(path).split(sep)
+    start_list = [x for x in abspath(start).split(sep) if x]
+    path_list = [x for x in abspath(path).split(sep) if x]
 
     # Work out how much of the filepath is shared by start and path.
     i = len(commonprefix([start_list, path_list]))
diff --git a/Lib/test/test_ntpath.py b/Lib/test/test_ntpath.py
index 73645f1..e1852c0 100644
--- a/Lib/test/test_ntpath.py
+++ b/Lib/test/test_ntpath.py
@@ -178,6 +178,16 @@
         tester('ntpath.relpath("a", "b/c")', '..\\..\\a')
         tester('ntpath.relpath("//conky/mountpoint/a", "//conky/mountpoint/b/c")', '..\\..\\a')
         tester('ntpath.relpath("a", "a")', '.')
+        tester('ntpath.relpath("/foo/bar/bat", "/x/y/z")', '..\\..\\..\\foo\\bar\\bat')
+        tester('ntpath.relpath("/foo/bar/bat", "/foo/bar")', 'bat')
+        tester('ntpath.relpath("/foo/bar/bat", "/")', 'foo\\bar\\bat')
+        tester('ntpath.relpath("/", "/foo/bar/bat")', '..\\..\\..')
+        tester('ntpath.relpath("/foo/bar/bat", "/x")', '..\\foo\\bar\\bat')
+        tester('ntpath.relpath("/x", "/foo/bar/bat")', '..\\..\\..\\x')
+        tester('ntpath.relpath("/", "/")', '.')
+        tester('ntpath.relpath("/a", "/a")', '.')
+        tester('ntpath.relpath("/a/b", "/a/b")', '.')
+        tester('ntpath.relpath("c:/foo", "C:/FOO")', '.')
 
 
 class NtCommonTest(test_genericpath.CommonTest):
diff --git a/Lib/test/test_posixpath.py b/Lib/test/test_posixpath.py
index 2288c48..8bb78d6 100644
--- a/Lib/test/test_posixpath.py
+++ b/Lib/test/test_posixpath.py
@@ -322,6 +322,15 @@
             self.assertEqual(posixpath.relpath("a/b", "../c"), "../"+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