diff --git a/secret_handshake/util.py b/secret_handshake/util.py
index 429f798..2f2e8e7 100644
--- a/secret_handshake/util.py
+++ b/secret_handshake/util.py
@@ -35,7 +35,7 @@ def inc_nonce(nonce: bytes) -> bytes:
 
     num = bytes_to_long(nonce) + 1
 
-    if num > 2**MAX_NONCE:
+    if num > 2**MAX_NONCE - 1:
         num = 0
 
     bnum = long_to_bytes(num)
diff --git a/tests/test_util.py b/tests/test_util.py
index 7928c14..b43b036 100644
--- a/tests/test_util.py
+++ b/tests/test_util.py
@@ -33,7 +33,13 @@ from secret_handshake.util import bytes_to_long, inc_nonce, long_to_bytes, split
 T = TypeVar("T")
 
 
-@pytest.mark.parametrize("in_,out", ((b"\x00\x00\x00\x00", b"\x00" * 23 + b"\x01"),))
+@pytest.mark.parametrize(
+    "in_,out",
+    (
+        (b"\x00\x00\x00\x00", b"\x00" * 23 + b"\x01"),
+        (b"\xff" * 24, b"\x00" * 24),
+    ),
+)
 def test_inc_nonce(in_: bytes, out: bytes) -> None:
     """Test the inc_nonce function"""