diff --git a/Lib/ssl.py b/Lib/ssl.py
index 4f291f4..9e88073 100644
--- a/Lib/ssl.py
+++ b/Lib/ssl.py
@@ -324,7 +324,9 @@
         from the socket module."""
 
         self._makefile_refs += 1
-        return _fileobject(self, mode, bufsize)
+        # close=True so as to decrement the reference count when done with
+        # the file-like object.
+        return _fileobject(self, mode, bufsize, close=True)