diff --git a/Lib/_collections_abc.py b/Lib/_collections_abc.py
index d92b848e943..bff58ad4a7f 100644
--- a/Lib/_collections_abc.py
+++ b/Lib/_collections_abc.py
@@ -696,6 +696,7 @@ class Set(Collection):
             hx = hash(x)
             h ^= (hx ^ (hx << 16) ^ 89869747)  * 3644798167
             h &= MASK
+        h ^= (h >> 11) ^ (h >> 25)
         h = h * 69069 + 907133923
         h &= MASK
         if h > MAX:
diff --git a/Lib/test/test_collections.py b/Lib/test/test_collections.py
index f98048b34a7..1f659d7d604 100644
--- a/Lib/test/test_collections.py
+++ b/Lib/test/test_collections.py
@@ -1801,6 +1801,18 @@ class TestCollectionABCs(ABCTestCase):
         self.assertTrue(f1 != l1)
         self.assertTrue(f1 != l2)
 
+    def test_Set_hash_matches_frozenset(self):
+        sets = [
+            {}, {1}, {None}, {-1}, {0.0}, {"abc"}, {1, 2, 3},
+            {10**100, 10**101}, {"a", "b", "ab", ""}, {False, True},
+            {object(), object(), object()}, {float("nan")},  {frozenset()},
+            {*range(1000)}, {*range(1000)} - {100, 200, 300},
+            {*range(sys.maxsize - 10, sys.maxsize + 10)},
+        ]
+        for s in sets:
+            fs = frozenset(s)
+            self.assertEqual(hash(fs), Set._hash(fs), msg=s)
+
     def test_Mapping(self):
         for sample in [dict]:
             self.assertIsInstance(sample(), Mapping)
diff --git a/Misc/NEWS.d/next/Library/2021-07-21-23-16-30.bpo-44704.iqHLxQ.rst b/Misc/NEWS.d/next/Library/2021-07-21-23-16-30.bpo-44704.iqHLxQ.rst
new file mode 100644
index 00000000000..586661876de
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2021-07-21-23-16-30.bpo-44704.iqHLxQ.rst
@@ -0,0 +1 @@
+The implementation of ``collections.abc.Set._hash()`` now matches that of ``frozenset.__hash__()``.
\ No newline at end of file