diff --git a/PIL/Image.py b/PIL/Image.py
index 60981cb3c..4e458dde5 100644
--- a/PIL/Image.py
+++ b/PIL/Image.py
@@ -565,6 +565,9 @@ class Image(object):
         except Exception as msg:
             logger.debug("Error closing: %s", msg)
 
+        if getattr(self, 'map', None):
+            self.map = None
+    
         # Instead of simply setting to None, we're setting up a
         # deferred error that will better explain that the core image
         # object is gone.
diff --git a/Tests/test_file_tiff.py b/Tests/test_file_tiff.py
index 12189a0eb..81f135115 100644
--- a/Tests/test_file_tiff.py
+++ b/Tests/test_file_tiff.py
@@ -490,6 +490,7 @@ class TestFileTiffW32(PillowTestCase):
         tmpfile = self.tempfile("temp.tif")
         import os
 
+        # this is an mmaped file. 
         with Image.open("Tests/images/uint16_1_4660.tif") as im:
             im.save(tmpfile)
 
@@ -499,7 +500,12 @@ class TestFileTiffW32(PillowTestCase):
         self.assertRaises(Exception, lambda: os.remove(tmpfile))
         im.load()
         self.assertTrue(fp.closed)
-        # this should not fail, as load should have closed the file. 
+
+        # this closes the mmap
+        im.close()
+        
+        # this should not fail, as load should have closed the file pointer,
+        # and close should have closed the mmap
         os.remove(tmpfile)
 
 if __name__ == '__main__':