diff --git a/Lib/test/test_binascii.py b/Lib/test/test_binascii.py
index 5b45f7d..d4a905a 100755
--- a/Lib/test/test_binascii.py
+++ b/Lib/test/test_binascii.py
@@ -1,6 +1,6 @@
 """Test the binascii C module."""
 
-from test_support import verify, verbose
+from test_support import verify, verbose, have_unicode
 import binascii
 
 # Show module doc string
@@ -112,7 +112,9 @@
     print 'expected TypeError not raised'
 
 # Verify the treatment of Unicode strings
-verify(binascii.hexlify(u'a') == '61', "hexlify failed for Unicode")
+if have_unicode:
+    verify(binascii.hexlify(unicode('a', 'ascii')) == '61', 
+           "hexlify failed for Unicode")
 
 # A test for SF bug 534347 (segfaults without the proper fix)
 try: