routes.MapRoute(
            "Index2Redirect",
            "HomeController/Index2",
            new { controller = "HomeController", action = "Index", id = "" }
        );

public class AbandonSessionAttribute: ActionFilterAttribute
{
   public void OnActionExecuting(ActionFilterContext context)
   {
      if (Session.User.IsAuthenticated || Session.Count > 0)   // <<-- this is the important line
      {
         Session.Clear();
         FormsAuthentication.SignOut(); // and so on
         context.Result = new RedirectResult("/Index2");
      }
   }
}

// now, if this is called with non-empty session, it will be cleared and user will be redirected again here
[AbandonSession]
public ActionResult Index2()
{
}

Index()
{
    expire all session and forms-Authententication cookies
}

Index2()
{
   if(Session.IsNewSession)
   {
      redirect to Index action
   }
   else
   {
     Show view
   }
}