diff --git a/Lib/gzip.py b/Lib/gzip.py
index e422773..8002b43 100644
--- a/Lib/gzip.py
+++ b/Lib/gzip.py
@@ -583,8 +583,7 @@ def main():
                 g = sys.stdout.buffer
             else:
                 if arg[-3:] != ".gz":
-                    print("filename doesn't end in .gz:", repr(arg))
-                    continue
+                    sys.exit("filename doesn't end in .gz:", repr(arg))
                 f = open(arg, "rb")
                 g = builtins.open(arg[:-3], "wb")
         else:
diff --git a/Lib/test/test_gzip.py b/Lib/test/test_gzip.py
index c3fa9b0..1bb8f7a 100644
--- a/Lib/test/test_gzip.py
+++ b/Lib/test/test_gzip.py
@@ -774,10 +774,10 @@ def test_decompress_infile_outfile(self):
         self.assertEqual(err, b'')
 
     def test_decompress_infile_outfile_error(self):
-        rc, out, err = assert_python_ok('-m', 'gzip', '-d', 'thisisatest.out')
-        self.assertIn(b"filename doesn't end in .gz:", out)
-        self.assertEqual(rc, 0)
-        self.assertEqual(err, b'')
+        rc, out, err = assert_python_failure('-m', 'gzip', '-d', 'thisisatest.out')
+        self.assertIn(b"filename doesn't end in .gz:", err)
+        self.assertEqual(rc, 1)
+        self.assertEqual(out, b'')
 
     @create_and_remove_directory(TEMPDIR)
     def test_compress_stdin_outfile(self):
diff --git a/Misc/NEWS.d/next/Library/2021-02-25-09-44-36.bpo-43316.k9Gyqn.rst b/Misc/NEWS.d/next/Library/2021-02-25-09-44-36.bpo-43316.k9Gyqn.rst
new file mode 100644
index 0000000..1f0d3c4
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2021-02-25-09-44-36.bpo-43316.k9Gyqn.rst
@@ -0,0 +1,3 @@
+The ``python -m gzip`` command line application now properly fails when
+detecting an unsupported extension. It exits with a non-zero exit code and
+prints an error message to stderr.