diff --git a/cbor2/types.py b/cbor2/types.py
index 04d1050b..b0ab530c 100644
--- a/cbor2/types.py
+++ b/cbor2/types.py
@@ -44,8 +44,8 @@ class CBORTag:
     __slots__ = 'tag', 'value'
 
     def __init__(self, tag, value):
-        if not isinstance(tag, int):
-            raise TypeError('CBORTag tags must be integer numbers')
+        if not isinstance(tag, int) or tag not in range(2**64):
+            raise TypeError('CBORTag tags must be positive integers less than 2**64')
         self.tag = tag
         self.value = value
 
diff --git a/tests/test_encoder.py b/tests/test_encoder.py
index 3e9346b2..6beaa220 100644
--- a/tests/test_encoder.py
+++ b/tests/test_encoder.py
@@ -520,3 +520,8 @@ def test_encode_stringrefs_dict(impl):
         'd81901' 'd81900'
     )
     assert impl.dumps(value, string_referencing=True, canonical=True) == expected
+
+
+def test_negative_tag(impl):
+    with pytest.raises(TypeError):
+        impl.dumps(impl.CBORTag(-1, 'value'))