diff --git a/examples/shor.py b/examples/shor.py
index a6ad08a2b8b..63bda4b5b73 100644
--- a/examples/shor.py
+++ b/examples/shor.py
@@ -268,6 +268,8 @@ def quantum_order_finder(x: int, n: int) -> Optional[int]:
     r = f.denominator
     if x**r % n != 1:
         return None  # pragma: no cover
+    while r % 2 == 0 and x ** (r // 2) > n:
+        r //= 2  # pragma: no cover
     return r