diff --git a/Lib/multiprocessing/util.py b/Lib/multiprocessing/util.py
index 5e501bd..20bba37 100644
--- a/Lib/multiprocessing/util.py
+++ b/Lib/multiprocessing/util.py
@@ -294,6 +294,8 @@
     global _exiting
 
     if not _exiting:
+        _exiting = True
+
         info('process shutting down')
         debug('running all "atexit" finalizers with priority >= 0')
         _run_finalizers(0)