diff --git a/Lib/fileinput.py b/Lib/fileinput.py
index 21c2d1f..02dc4c6 100644
--- a/Lib/fileinput.py
+++ b/Lib/fileinput.py
@@ -233,8 +233,10 @@
         self.close()
 
     def close(self):
-        self.nextfile()
-        self._files = ()
+        try:
+            self.nextfile()
+        finally:
+            self._files = ()
 
     def __iter__(self):
         return self
@@ -270,23 +272,25 @@
 
         output = self._output
         self._output = 0
-        if output:
-            output.close()
+        try:
+            if output:
+                output.close()
+        finally:
+            file = self._file
+            self._file = 0
+            try:
+                if file and not self._isstdin:
+                    file.close()
+            finally:
+                backupfilename = self._backupfilename
+                self._backupfilename = 0
+                if backupfilename and not self._backup:
+                    try: os.unlink(backupfilename)
+                    except OSError: pass
 
-        file = self._file
-        self._file = 0
-        if file and not self._isstdin:
-            file.close()
-
-        backupfilename = self._backupfilename
-        self._backupfilename = 0
-        if backupfilename and not self._backup:
-            try: os.unlink(backupfilename)
-            except OSError: pass
-
-        self._isstdin = False
-        self._buffer = []
-        self._bufindex = 0
+                self._isstdin = False
+                self._buffer = []
+                self._bufindex = 0
 
     def readline(self):
         try: