diff --git a/email_validator/syntax.py b/email_validator/syntax.py
index 0a06840..f7e49e2 100644
--- a/email_validator/syntax.py
+++ b/email_validator/syntax.py
@@ -178,7 +178,7 @@ def unquote_quoted_string(text: str) -> tuple[str, bool]:
             raise EmailSyntaxError("There can't be anything after the email address.")
 
         # Remove the initial and trailing angle brackets.
-        addr_spec = right_part[1:].rstrip(">")
+        addr_spec = right_part[1:-1]
 
         # Split the email address at the first unquoted @-sign.
         local_part, domain_part = split_string_at_unquoted_special(addr_spec, ("@",))
diff --git a/tests/test_syntax.py b/tests/test_syntax.py
index a322f4e..8f73038 100644
--- a/tests/test_syntax.py
+++ b/tests/test_syntax.py
@@ -518,6 +518,20 @@ def test_email_invalid_syntax_strict(email_input: str, error_msg: str) -> None:
     assert str(exc_info.value) == error_msg
 
 
+@pytest.mark.parametrize(
+    'email_input',
+    [
+        '<me@example.com>>',
+        'Display Name <me@example.com>>',
+        'Display Name <me@example.com>>>',
+    ])
+def test_email_invalid_syntax_display_name(email_input: str) -> None:
+    # Only one close angle bracket may follow the address.
+    with pytest.raises(EmailSyntaxError) as exc_info:
+        validate_email(email_input, check_deliverability=False, allow_display_name=True)
+    assert str(exc_info.value) == "The part after the @-sign contains invalid characters: '>'."
+
+
 @pytest.mark.parametrize(
     'email_input',
     [