diff --git a/Misc/NEWS.d/next/C API/2020-03-12-00-27-26.bpo-39884.CGOJBO.rst b/Misc/NEWS.d/next/C API/2020-03-12-00-27-26.bpo-39884.CGOJBO.rst
new file mode 100644
index 0000000..c65dfdc
--- /dev/null
+++ b/Misc/NEWS.d/next/C API/2020-03-12-00-27-26.bpo-39884.CGOJBO.rst
@@ -0,0 +1,2 @@
+:c:func:`PyDescr_NewMethod` and :c:func:`PyCFunction_NewEx` now include the
+method name in the SystemError "bad call flags" error message to ease debug.
diff --git a/Objects/descrobject.c b/Objects/descrobject.c
index 4ebbb74..b448ec6 100644
--- a/Objects/descrobject.c
+++ b/Objects/descrobject.c
@@ -888,7 +888,8 @@
             vectorcall = method_vectorcall_O;
             break;
         default:
-            PyErr_SetString(PyExc_SystemError, "bad call flags");
+            PyErr_Format(PyExc_SystemError,
+                         "%s() method: bad call flags", method->ml_name);
             return NULL;
     }
 
diff --git a/Objects/methodobject.c b/Objects/methodobject.c
index 0d45705..16abded 100644
--- a/Objects/methodobject.c
+++ b/Objects/methodobject.c
@@ -56,7 +56,8 @@
             vectorcall = cfunction_vectorcall_O;
             break;
         default:
-            PyErr_SetString(PyExc_SystemError, "bad call flags");
+            PyErr_Format(PyExc_SystemError,
+                         "%s() method: bad call flags", ml->ml_name);
             return NULL;
     }