diff --git a/Lib/multiprocessing/process.py b/Lib/multiprocessing/process.py
index 16c4e1e..11c8fca 100644
--- a/Lib/multiprocessing/process.py
+++ b/Lib/multiprocessing/process.py
@@ -156,10 +156,16 @@
         if self is _current_process:
             return True
         assert self._parent_pid == os.getpid(), 'can only test a child process'
+
         if self._popen is None:
             return False
-        self._popen.poll()
-        return self._popen.returncode is None
+
+        returncode = self._popen.poll()
+        if returncode is None:
+            return True
+        else:
+            _current_process._children.discard(self)
+            return False
 
     @property
     def name(self):