The iOS 5.1.1 now can be a jailbreak as untethered with Absinthe 2.0.4 version. Absinthe jailbreak tool released by Chronic Dev Team. So Absinthe 2.0 is familiar with all Devices except Apple TV3 and Absinthe are supports both Windows and Mac operating system.
Supports Devices for Absinthe 2.0 untethered jailbreak.
iPhone 3Gs /iPhone 4 / iPhone 4 CDMA / iPhone 4S
iPad 1/ iPad 2 WiFi /iPad 2 GSM / iPad 2 CDMA / iPad 2 WiFi / iPad 3 WiFi
iPad 3 Global / iPad 3 CDMA
iPod 3G /iPod 4G
Apple TV models
So Absinthe 2.0.4 only supports iOS 5.1.1 version, if you are running below iOS 5.1.1 version, you should update your Device to 5.1.1 version.
How to jailbreak?
So before the start jailbreak process, highly recommended to backup all your data. When you use any of a jailbreak tools, you should put your Device in to DFU mode, However, Absinthe is not required to put your Device in to DFU mode, it will not take more than 10 minutes to jailbreak your Device. You should Download Absinthe 2.0.4 version to jailbreak 5.1.1 as untethered. Please grab your Download file according to your operation system.
watch below video demo and this is a full step guide how to jailbreak?