diff --git a/Lib/test/test_types.py b/Lib/test/test_types.py
index 3f7677108ef2a8..bb504122ba7968 100644
--- a/Lib/test/test_types.py
+++ b/Lib/test/test_types.py
@@ -663,6 +663,10 @@ def test_or_types_operator(self):
             x.__args__ = [str, int]
             (int | str ) == x
 
+    def test_hash(self):
+        self.assertEqual(hash(int | str), hash(str | int))
+        self.assertEqual(hash(int | str), hash(typing.Union[int, str]))
+
     def test_instancecheck(self):
         x = int | str
         self.assertIsInstance(1, x)
diff --git a/Misc/NEWS.d/next/Core and Builtins/2021-07-16-09-59-13.bpo-44646.Yb6s05.rst b/Misc/NEWS.d/next/Core and Builtins/2021-07-16-09-59-13.bpo-44646.Yb6s05.rst
new file mode 100644
index 00000000000000..0e28eac54fe987
--- /dev/null
+++ b/Misc/NEWS.d/next/Core and Builtins/2021-07-16-09-59-13.bpo-44646.Yb6s05.rst	
@@ -0,0 +1,2 @@
+Fix the hash of the union type: it no longer depends on the order of
+arguments.
diff --git a/Objects/unionobject.c b/Objects/unionobject.c
index 229b518ea75756..762df5d9780a38 100644
--- a/Objects/unionobject.c
+++ b/Objects/unionobject.c
@@ -33,11 +33,13 @@ static Py_hash_t
 union_hash(PyObject *self)
 {
     unionobject *alias = (unionobject *)self;
-    Py_hash_t h1 = PyObject_Hash(alias->args);
-    if (h1 == -1) {
-        return -1;
+    PyObject *args = PyFrozenSet_New(alias->args);
+    if (args == NULL) {
+        return (Py_hash_t)-1;
     }
-    return h1;
+    Py_hash_t hash = PyObject_Hash(args);
+    Py_DECREF(args);
+    return hash;
 }
 
 static int