diff --git a/idna/core.py b/idna/core.py
index 871ebd3..c66fb9f 100644
--- a/idna/core.py
+++ b/idna/core.py
@@ -312,7 +312,10 @@ def ulabel(label):
         check_label(label_bytes)
         return label_bytes.decode('ascii')
 
-    label = label_bytes.decode('punycode')
+    try:
+        label = label_bytes.decode('punycode')
+    except UnicodeError:
+        raise IDNAError('Invalid A-label')
     check_label(label)
     return label
 
diff --git a/tests/test_idna.py b/tests/test_idna.py
index 7ac6057..f0c74d2 100755
--- a/tests/test_idna.py
+++ b/tests/test_idna.py
@@ -260,6 +260,7 @@ def test_decode(self):
         self.assertRaises(idna.IDNAError, idna.decode, 'xn---------90gglbagaac.aa')
         self.assertRaises(idna.IDNAError, idna.decode, 'xn--')
         self.assertRaises(idna.IDNAError, idna.decode, b'\x8d\xd2')
+        self.assertRaises(idna.IDNAError, idna.decode, b'A.A.0.a.a.A.0.a.A.A.0.a.A.0A.2.a.A.A.0.a.A.0.A.a.A0.a.a.A.0.a.fB.A.A.a.A.A.B.A.A.a.A.A.B.A.A.a.A.A.0.a.A.a.a.A.A.0.a.A.0.A.a.A0.a.a.A.0.a.fB.A.A.a.A.A.B.0A.A.a.A.A.B.A.A.a.A.A.a.A.A.B.A.A.a.A.0.a.B.A.A.a.A.B.A.a.A.A.5.a.A.0.a.Ba.A.B.A.A.a.A.0.a.Xn--B.A.A.A.a')
 
 if __name__ == '__main__':
     unittest.main()