diff --git a/Lib/test/test_codecs.py b/Lib/test/test_codecs.py
index f6823805fee..f9c9e69f232 100644
--- a/Lib/test/test_codecs.py
+++ b/Lib/test/test_codecs.py
@@ -2335,7 +2335,7 @@ def test_seek0(self):
 try:
     import zlib
 except ImportError:
-    pass
+    zlib = None
 else:
     bytes_transform_encodings.append("zlib_codec")
     transform_aliases["zlib_codec"] = ["zip", "zlib"]
@@ -2440,6 +2440,7 @@ def test_binary_to_text_blacklists_text_transforms(self):
                     bad_input.decode("rot_13")
                 self.assertIsNone(failure.exception.__cause__)
 
+    @unittest.skipUnless(zlib, "Requires zlib support")
     def test_custom_zlib_error_is_wrapped(self):
         # Check zlib codec gives a good error for malformed input
         msg = "^decoding with 'zlib_codec' codec failed"