diff --git a/github/client.py b/github/client.py
index bbd7032..d5ca29d 100644
--- a/github/client.py
+++ b/github/client.py
@@ -104,13 +104,10 @@ class GHClient:
     async def __aexit__(self, *args: Any, **kwargs: Any) -> None:
         try:
             session = self.http.session
-            await self.session.close()
+            await session.close()
         except Exception as exc:
             raise Exception('HTTP Session doesn\'t exist') from exc
 
-        if session := getattr(self.http, 'session', None):
-            await session.close()
-
     def __repr__(self) -> str:
         return f'<{self.__class__.__name__} has_auth={bool(self._auth)}>'