diff --git a/Lib/logging/handlers.py b/Lib/logging/handlers.py
index 472eee5..f8c7164 100644
--- a/Lib/logging/handlers.py
+++ b/Lib/logging/handlers.py
@@ -125,6 +125,7 @@
         """
         if self.stream:
             self.stream.close()
+            self.stream = None
         if self.backupCount > 0:
             for i in range(self.backupCount - 1, 0, -1):
                 sfn = "%s.%d" % (self.baseFilename, i)
@@ -324,6 +325,7 @@
         """
         if self.stream:
             self.stream.close()
+            self.stream = None
         # get the time that this sequence started at and make it a TimeTuple
         t = self.rolloverAt - self.interval
         if self.utc: