Index: Lib/unittest/test/test_case.py
===================================================================
--- Lib/unittest/test/test_case.py	(revision 86592)
+++ Lib/unittest/test/test_case.py	(working copy)
@@ -712,6 +712,13 @@
         self.assertRaises(self.failureException, self.assertItemsEqual,
                           [1, {'b': 2}, None, True], [{'b': 2}, True, None])
 
+        # Same elements which don't reliably compare, in
+        # different order, see issue 10242
+        a = [{2,4}, {1,2}]
+        b = a[::-1]
+        self.assertItemsEqual(a, b)
+
+
     def testAssertSetEqual(self):
         set1 = set()
         set2 = set()
Index: Lib/unittest/case.py
===================================================================
--- Lib/unittest/case.py	(revision 86592)
+++ Lib/unittest/case.py	(working copy)
@@ -6,6 +6,7 @@
 import pprint
 import re
 import warnings
+import collections
 
 from . import result
 from .util import (strclass, safe_repr, sorted_list_difference,
@@ -1002,8 +1003,8 @@
 
     def assertItemsEqual(self, expected_seq, actual_seq, msg=None):
         """An unordered sequence / set specific comparison. It asserts that
-        expected_seq and actual_seq contain the same elements. It is
-        the equivalent of::
+        expected_seq and actual_seq contain the same elements in the same
+        quantities. It is the equivalent of::
 
             self.assertEqual(sorted(expected_seq), sorted(actual_seq))
 
@@ -1016,15 +1017,19 @@
             - [0, 0, 1] and [0, 1] compare unequal.
         """
         try:
-            expected = sorted(expected_seq)
-            actual = sorted(actual_seq)
+            expected_cnt = collections.Counter(iter(expected_seq))
+            actual_cnt = collections.Counter(iter(actual_seq))
         except TypeError:
             # Unsortable items (example: set(), complex(), ...)
             expected = list(expected_seq)
             actual = list(actual_seq)
             missing, unexpected = unorderable_list_difference(expected, actual)
         else:
-            return self.assertSequenceEqual(expected, actual, msg=msg)
+            if expected_cnt == actual_cnt:
+                return
+            else:
+                missing = [i for i in expected_cnt if expected_cnt[i] != actual_cnt[i]]
+                unexpected = [i for i in actual_cnt if actual_cnt[i] != expected_cnt[i]]
 
         errors = []
         if missing: