diff --git a/Lib/test/support.py b/Lib/test/support.py
--- a/Lib/test/support.py
+++ b/Lib/test/support.py
@@ -24,6 +24,7 @@
 import fnmatch
 import logging.handlers
 import struct
+import tempfile
 
 try:
     import _thread, threading
@@ -1694,9 +1695,13 @@
     if not hasattr(os, "setxattr"):
         can = False
     else:
+        tmp_fp, tmp_name = tempfile.mkstemp()
         try:
             with open(TESTFN, "wb") as fp:
                 try:
+                    # TESTFN & tempfile may use different file systems with
+                    # different capabilities
+                    os.fsetxattr(tmp_fp, b"user.test", b"")
                     os.fsetxattr(fp.fileno(), b"user.test", b"")
                     # Kernels < 2.6.39 don't respect setxattr flags.
                     kernel_version = platform.release()
@@ -1706,6 +1711,7 @@
                     can = False
         finally:
             unlink(TESTFN)
+            unlink(tmp_name)
     _can_xattr = can
     return can