diff --git a/Lib/mailbox.py b/Lib/mailbox.py
index ba49753..3866953 100644
--- a/Lib/mailbox.py
+++ b/Lib/mailbox.py
@@ -719,10 +719,14 @@
 
     def close(self):
         """Flush and close the mailbox."""
-        self.flush()
-        if self._locked:
-            self.unlock()
-        self._file.close()  # Sync has been done by self.flush() above.
+        try:
+            self.flush()
+        finally:
+            try:
+                if self._locked:
+                    self.unlock()
+            finally:
+                self._file.close()  # Sync has been done by self.flush() above.
 
     def _lookup(self, key=None):
         """Return (start, stop) or raise KeyError."""