diff --git a/Doc/whatsnew/3.9.rst b/Doc/whatsnew/3.9.rst
index 542a0319600..281173edb89 100644
--- a/Doc/whatsnew/3.9.rst
+++ b/Doc/whatsnew/3.9.rst
@@ -217,6 +217,7 @@ Build and C API Changes
   ``PyThreadState.recursion_depth`` field. Remove ``_Py_CheckRecursionLimit``
   from the stable ABI.
   (Contributed by Victor Stinner in :issue:`38644`.)
+
 * Add a new public :c:func:`PyObject_CallNoArgs` function to the C API, which
   calls a callable Python object without any arguments. It is the most efficient
   way to call a callable Python object without any argument.
@@ -230,6 +231,10 @@ Build and C API Changes
   ``pyfpe.h`` from ``Py_LIMITED_API`` (stable API).
   (Contributed by Victor Stinner in :issue:`38835`.)
 
+* Remove ``PyMethod_ClearFreeList()`` and ``PyCFunction_ClearFreeList()``
+  functions: the free lists of bound method objects have been removed.
+  (Contributed by Inada Naoki and Victor Stinner in :issue:`37340`.)
+
 
 Deprecated
 ==========
diff --git a/Include/classobject.h b/Include/classobject.h
index c83303c3900..840431a1276 100644
--- a/Include/classobject.h
+++ b/Include/classobject.h
@@ -33,8 +33,6 @@ PyAPI_FUNC(PyObject *) PyMethod_Self(PyObject *);
 #define PyMethod_GET_SELF(meth) \
         (((PyMethodObject *)meth) -> im_self)
 
-PyAPI_FUNC(int) PyMethod_ClearFreeList(void);
-
 typedef struct {
     PyObject_HEAD
     PyObject *func;
diff --git a/Include/internal/pycore_pylifecycle.h b/Include/internal/pycore_pylifecycle.h
index b8d5e361b3c..c837bcdbc03 100644
--- a/Include/internal/pycore_pylifecycle.h
+++ b/Include/internal/pycore_pylifecycle.h
@@ -59,9 +59,7 @@ extern PyStatus _PyGC_Init(PyThreadState *tstate);
 
 /* Various internal finalizers */
 
-extern void _PyMethod_Fini(void);
 extern void _PyFrame_Fini(void);
-extern void _PyCFunction_Fini(void);
 extern void _PyDict_Fini(void);
 extern void _PyTuple_Fini(void);
 extern void _PyList_Fini(void);
diff --git a/Include/methodobject.h b/Include/methodobject.h
index 3bccf5a3f60..a15d05f8991 100644
--- a/Include/methodobject.h
+++ b/Include/methodobject.h
@@ -97,8 +97,6 @@ typedef struct {
 } PyCFunctionObject;
 #endif
 
-PyAPI_FUNC(int) PyCFunction_ClearFreeList(void);
-
 #ifdef __cplusplus
 }
 #endif
diff --git a/Misc/NEWS.d/next/C API/2019-11-20-11-08-06.bpo-37340.JBQJMS.rst b/Misc/NEWS.d/next/C API/2019-11-20-11-08-06.bpo-37340.JBQJMS.rst
new file mode 100644
index 00000000000..8ffa4eb12bd
--- /dev/null
+++ b/Misc/NEWS.d/next/C API/2019-11-20-11-08-06.bpo-37340.JBQJMS.rst	
@@ -0,0 +1,2 @@
+Remove ``PyMethod_ClearFreeList()`` and ``PyCFunction_ClearFreeList()``
+functions: the free lists of bound method objects have been removed.
diff --git a/Modules/gcmodule.c b/Modules/gcmodule.c
index 967bbe9c0d4..d232179a11c 100644
--- a/Modules/gcmodule.c
+++ b/Modules/gcmodule.c
@@ -1029,9 +1029,7 @@ delete_garbage(PyThreadState *tstate, GCState *gcstate,
 static void
 clear_freelists(void)
 {
-    (void)PyMethod_ClearFreeList();
     (void)PyFrame_ClearFreeList();
-    (void)PyCFunction_ClearFreeList();
     (void)PyTuple_ClearFreeList();
     (void)PyUnicode_ClearFreeList();
     (void)PyFloat_ClearFreeList();
diff --git a/Objects/classobject.c b/Objects/classobject.c
index d3fc7264154..db53f04862c 100644
--- a/Objects/classobject.c
+++ b/Objects/classobject.c
@@ -371,20 +371,6 @@ PyTypeObject PyMethod_Type = {
     method_new,                                 /* tp_new */
 };
 
-/* Clear out the free list */
-
-int
-PyMethod_ClearFreeList(void)
-{
-    return 0;
-}
-
-void
-_PyMethod_Fini(void)
-{
-    (void)PyMethod_ClearFreeList();
-}
-
 /* ------------------------------------------------------------------------
  * instance method
  */
diff --git a/Objects/methodobject.c b/Objects/methodobject.c
index 8f752c610ce..6a37238d86d 100644
--- a/Objects/methodobject.c
+++ b/Objects/methodobject.c
@@ -313,21 +313,6 @@ PyTypeObject PyCFunction_Type = {
     0,                                          /* tp_dict */
 };
 
-/* Clear out the free list */
-
-int
-PyCFunction_ClearFreeList(void)
-{
-    return 0;
-}
-
-void
-_PyCFunction_Fini(void)
-{
-    (void)PyCFunction_ClearFreeList();
-}
-
-
 /* Vectorcall functions for each of the PyCFunction calling conventions,
  * except for METH_VARARGS (possibly combined with METH_KEYWORDS) which
  * doesn't use vectorcall.
diff --git a/Python/pylifecycle.c b/Python/pylifecycle.c
index 2149dbf569d..44a4b18590b 100644
--- a/Python/pylifecycle.c
+++ b/Python/pylifecycle.c
@@ -1173,9 +1173,7 @@ finalize_interp_types(PyThreadState *tstate, int is_main_interp)
 {
     if (is_main_interp) {
         /* Sundry finalizers */
-        _PyMethod_Fini();
         _PyFrame_Fini();
-        _PyCFunction_Fini();
         _PyTuple_Fini();
         _PyList_Fini();
         _PySet_Fini();