diff --git a/Lib/tarfile.py b/Lib/tarfile.py
index b5f9f30..1b8f140 100644
--- a/Lib/tarfile.py
+++ b/Lib/tarfile.py
@@ -857,7 +857,11 @@
         if self.name.endswith("/"):
             type = DIRTYPE
 
-        name = normpath(self.name)
+        if type in (GNUTYPE_LONGNAME, GNUTYPE_LONGLINK):
+            # Prevent "././@LongLink" from being normalized.
+            name = self.name
+        else:
+            name = normpath(self.name)
 
         if type == DIRTYPE:
             # directories should end with '/'
@@ -913,7 +917,7 @@
         ]
 
         buf += struct.pack("%ds" % BLOCKSIZE, "".join(parts))
-        chksum = calc_chksums(buf)[0]
+        chksum = calc_chksums(buf[-BLOCKSIZE:])[0]
         buf = buf[:-364] + "%06o\0" % chksum + buf[-357:]
         self.buf = buf
         return buf
diff --git a/Lib/test/test_tarfile.py b/Lib/test/test_tarfile.py
index ee83cbe..2685d67 100644
--- a/Lib/test/test_tarfile.py
+++ b/Lib/test/test_tarfile.py
@@ -388,13 +388,6 @@
        is tested as well.
     """
 
-    def setUp(self):
-        self.tar = tarfile.open(tmpname(), "w")
-        self.tar.posix = False
-
-    def tearDown(self):
-        self.tar.close()
-
     def _length(self, s):
         blocks, remainder = divmod(len(s) + 1, 512)
         if remainder:
@@ -423,12 +416,23 @@
             tarinfo.linkname = link
             tarinfo.type = tarfile.LNKTYPE
 
-        self.tar.addfile(tarinfo)
+        tar = tarfile.open(tmpname(), "w")
+        tar.posix = False
+        tar.addfile(tarinfo)
 
         v1 = self._calc_size(name, link)
-        v2 = self.tar.offset
+        v2 = tar.offset
         self.assertEqual(v1, v2, "GNU longname/longlink creation failed")
 
+        tar.close()
+
+        tar = tarfile.open(tmpname())
+        member = tar.next()
+        self.failIf(member is None, "unable to read longname member")
+        self.assert_(tarinfo.name == member.name and \
+                     tarinfo.linkname == member.linkname, \
+                     "unable to read longname member")
+
     def test_longname_1023(self):
         self._test(("longnam/" * 127) + "longnam")