diff --git a/Lib/posixpath.py b/Lib/posixpath.py
index d089809d998..b1e1a9255e6 100644
--- a/Lib/posixpath.py
+++ b/Lib/posixpath.py
@@ -418,9 +418,11 @@ def _joinrealpath(path, rest, seen):
         if name == pardir:
             # parent dir
             if path:
-                path = dirname(path)
+                path, name = split(path)
+                if name == pardir:
+                    path = join(path, pardir, pardir)
             else:
-                path = name
+                path = pardir
             continue
         newpath = join(path, name)
         if not islink(newpath):
diff --git a/Lib/test/test_posixpath.py b/Lib/test/test_posixpath.py
index 3af91759004..01d84daa211 100644
--- a/Lib/test/test_posixpath.py
+++ b/Lib/test/test_posixpath.py
@@ -340,6 +340,24 @@ class PosixPathTest(unittest.TestCase):
         self.assertEqual(posixpath.normpath(b"///..//./foo/.//bar"),
                          b"/foo/bar")
 
+    def test_realpath_curdir(self):
+        self.assertEqual(realpath('.'), os.getcwd())
+        self.assertEqual(realpath('./.'), os.getcwd())
+        self.assertEqual(realpath('/'.join(['.'] * 100)), os.getcwd())
+
+        self.assertEqual(realpath(b'.'), os.getcwdb())
+        self.assertEqual(realpath(b'./.'), os.getcwdb())
+        self.assertEqual(realpath(b'/'.join([b'.'] * 100)), os.getcwdb())
+
+    def test_realpath_pardir(self):
+        self.assertEqual(realpath('..'), dirname(os.getcwd()))
+        self.assertEqual(realpath('../..'), dirname(dirname(os.getcwd())))
+        self.assertEqual(realpath('/'.join(['..'] * 100)), '/')
+
+        self.assertEqual(realpath(b'..'), dirname(os.getcwdb()))
+        self.assertEqual(realpath(b'../..'), dirname(dirname(os.getcwdb())))
+        self.assertEqual(realpath(b'/'.join([b'..'] * 100)), b'/')
+
     @unittest.skipUnless(hasattr(os, "symlink"),
                          "Missing symlink implementation")
     @skip_if_ABSTFN_contains_backslash