diff --git a/Modules/_pickle.c b/Modules/_pickle.c
--- a/Modules/_pickle.c
+++ b/Modules/_pickle.c
@@ -7411,6 +7411,13 @@
 }
 
 static int
+pickle_free(PyObject *m)
+{
+    _Pickle_ClearState(_Pickle_GetState(m));
+    return 0;
+}
+
+static int
 pickle_traverse(PyObject *m, visitproc visit, void *arg)
 {
     PickleState *st = _Pickle_GetState(m);
@@ -7440,7 +7447,7 @@
     NULL,                /* m_reload */
     pickle_traverse,     /* m_traverse */
     pickle_clear,        /* m_clear */
-    NULL                 /* m_free */
+    (freefunc)pickle_free /* m_free */
 };
 
 PyMODINIT_FUNC