Can an iPhone 4 on 4.1 to 5.1.1 still be upgraded?

kumag

I have a brother who never updated his iPhone and was stuck on 4.1 jailbroken. He asked me if I can update it and still jailbreak it I said on 6.0.1 but tethered. He said he doesn't want tethered. Now does anyone know if it is still possible to update it to 5.1.1 even though it is no longer signed by apple. Hope someone can advise me with this. Thanks in advance