diff --git a/gymnasium/core.py b/gymnasium/core.py
index 483fdfe36..aaf9476f7 100644
--- a/gymnasium/core.py
+++ b/gymnasium/core.py
@@ -447,8 +447,8 @@ def set_wrapper_attr(self, name: str, value: Any):
         # check if the base environment has the wrapper, otherwise, we set it on the top (this) wrapper
         if hasattr(sub_env, name):
             setattr(sub_env, name, value)
-
-        setattr(self, name, value)
+        else:
+            setattr(self, name, value)
 
     def __str__(self):
         """Returns the wrapper name and the :attr:`env` representation string."""