diff --git a/Misc/NEWS b/Misc/NEWS
index 889cead8a69..1bb4f6f4f91 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -80,6 +80,8 @@ C API
 Library
 -------
 
+- Issue #3660: fix a memory leak in the C accelerator of the pickle module.
+
 - Issue #3160: the "bdist_wininst" distutils command didn't work.
 
 - Issue #1658: tkinter changes dict size during iteration in both
diff --git a/Modules/_pickle.c b/Modules/_pickle.c
index ea5bbe2759a..f7b52128638 100644
--- a/Modules/_pickle.c
+++ b/Modules/_pickle.c
@@ -3837,13 +3837,17 @@ load_build(UnpicklerObject *self)
     if (setstate == NULL) {
         if (PyErr_ExceptionMatches(PyExc_AttributeError))
             PyErr_Clear();
-        else
+        else {
+            Py_DECREF(state);
             return -1;
+        }
     }
     else {
         PyObject *result;
 
         /* The explicit __setstate__ is responsible for everything. */
+        /* Ugh... this does not leak since unpickler_call() steals the
+           reference to state first. */
         result = unpickler_call(self, setstate, state);
         Py_DECREF(setstate);
         if (result == NULL)