Index: Lib/unittest/test/test_case.py
===================================================================
--- Lib/unittest/test/test_case.py	(revision 86620)
+++ Lib/unittest/test/test_case.py	(working copy)
@@ -711,7 +711,13 @@
         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 86620)
+++ Lib/unittest/case.py	(working copy)
@@ -6,6 +6,7 @@
 import pprint
 import re
 import warnings
+import collections
 
 from . import result
 from .util import (
@@ -843,8 +844,8 @@
 
     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))
 
@@ -864,8 +865,8 @@
                              "comparing unequal types"]:
                     warnings.filterwarnings("ignore", _msg, DeprecationWarning)
             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)
@@ -874,7 +875,8 @@
                     expected, actual, ignore_duplicate=False
                 )
             else:
-                return self.assertSequenceEqual(expected, actual, msg=msg)
+                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: