Warning: Backup of your iPhone 4S through iTunes before proceeding, because you may lose Camera Roll during this process.
Untethered Jailbreak iPhone 4S over iOS 5.0.1 with Absinthe
Download Absinthe, extract its contents and double click “Absinthe” app icon to launch it
Connect your iPhone 4S to computer through USB
Click on “Jailbreak” button
Absinthe will take you through several steps of the jailbreak process, so don’t worry and just pass those patiently like the Initial data sending, Restoring in progress, iPhone 4S reboot, Wait to finish booting, Preparing jailbreak data, and Sending payload data
“Almost done” message will display on Absinthe screen
On Homescreen of your iPhone 4S, locate Absinthe icon and tap on that
If you find an error message because of server down, then tap on “Settings” app on home screen of your iPhone 4S and turn on VPN
Configuration error message will display, but wait for a minute and your iPhone 4S will reboot
“Cydia” will display on your iPhone 4S home screen and done.