diff --git a/Lib/email/quoprimime.py b/Lib/email/quoprimime.py
index b9dbfa97e04..0c18a9e04ef 100644
--- a/Lib/email/quoprimime.py
+++ b/Lib/email/quoprimime.py
@@ -333,4 +333,4 @@ def header_decode(s):
     the high level email.header class for that functionality.
     """
     s = s.replace('_', ' ')
-    return re.sub(r'=\w{2}', _unquote_match, s)
+    return re.sub(r'=[a-fA-F0-9]{2}', _unquote_match, s)
diff --git a/Lib/email/test/test_email.py b/Lib/email/test/test_email.py
index 300fc21711c..c3610bf6e24 100644
--- a/Lib/email/test/test_email.py
+++ b/Lib/email/test/test_email.py
@@ -1621,6 +1621,12 @@ class TestRFC2047(unittest.TestCase):
             dh = decode_header(s % q)
             self.assertEqual(dh, [(a, 'iso-8859-1')])
 
+    def test_rfc2047_Q_invalid_digits(self):
+        # issue 10004.
+        s = '=?iso-8659-1?Q?andr=e9=zz?='
+        self.assertEqual(decode_header(s),
+                        [(b'andr\xe9=zz', 'iso-8659-1')])
+
 
 # Test the MIMEMessage class
 class TestMIMEMessage(TestEmailBase):
diff --git a/Misc/NEWS b/Misc/NEWS
index d30b05b3a63..78eb34f920d 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -48,6 +48,9 @@ Core and Builtins
 Library
 -------
 
+- Issue #10004: quoprimime no longer generates a traceback when confronted
+  with invalid characters after '=' in a Q-encoded word.
+
 - Issue #9950: Fix socket.sendall() crash or misbehaviour when a signal is
   received.  Now sendall() properly calls signal handlers if necessary,
   and retries sending if these returned successfully, including on sockets