diff --git a/Lib/ntpath.py b/Lib/ntpath.py
index 37f32f0..02d8584 100644
--- a/Lib/ntpath.py
+++ b/Lib/ntpath.py
@@ -397,6 +397,8 @@
 
 def normpath(path):
     """Normalize path, eliminating double slashes, etc."""
+    # Preserve unicode (if path is unicode)
+    backslash, dot = (u'\\', u'.') if isinstance(path, unicode) else ('\\', '.')
     path = path.replace("/", "\\")
     prefix, path = splitdrive(path)
     # We need to be careful here. If the prefix is empty, and the path starts
@@ -411,12 +413,12 @@
     if prefix == '':
         # No drive letter - preserve initial backslashes
         while path[:1] == "\\":
-            prefix = prefix + "\\"
+            prefix = prefix + backslash
             path = path[1:]
     else:
         # We have a drive letter - collapse initial backslashes
         if path.startswith("\\"):
-            prefix = prefix + "\\"
+            prefix = prefix + backslash
             path = path.lstrip("\\")
     comps = path.split("\\")
     i = 0
@@ -435,8 +437,8 @@
             i += 1
     # If the path is now empty, substitute '.'
     if not prefix and not comps:
-        comps.append('.')
-    return prefix + "\\".join(comps)
+        comps.append(dot)
+    return prefix + backslash.join(comps)
 
 
 # Return an absolute path.
diff --git a/Lib/posixpath.py b/Lib/posixpath.py
index cdce5af..35dcffb 100644
--- a/Lib/posixpath.py
+++ b/Lib/posixpath.py
@@ -307,8 +307,10 @@
 
 def normpath(path):
     """Normalize path, eliminating double slashes, etc."""
+    # Preserve unicode (if path is unicode)
+    slash, dot = (u'/', u'.') if isinstance(path, unicode) else ('/', '.')
     if path == '':
-        return '.'
+        return dot
     initial_slashes = path.startswith('/')
     # POSIX allows one or two initial slashes, but treats three or more
     # as single slash.
@@ -326,10 +328,10 @@
         elif new_comps:
             new_comps.pop()
     comps = new_comps
-    path = '/'.join(comps)
+    path = slash.join(comps)
     if initial_slashes:
-        path = '/'*initial_slashes + path
-    return path or '.'
+        path = slash*initial_slashes + path
+    return path or dot
 
 
 def abspath(path):
diff --git a/Lib/test/test_ntpath.py b/Lib/test/test_ntpath.py
index a077c78..10bbe3a 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):
         oldenv = os.environ.copy()
         try:
diff --git a/Lib/test/test_posixpath.py b/Lib/test/test_posixpath.py
index b7fbd50..f6cb047 100644
--- a/Lib/test/test_posixpath.py
+++ b/Lib/test/test_posixpath.py
@@ -385,6 +385,11 @@
         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):