But before going into the steps, you should now that updating your iOS to iOS 5.1.1 will also update your existing baseband therefore will close the chance to unlock your device. Therefore, it's recommended when you are on iOS 5.1.1, then save your iOS 5.1.1 SHSH blobs.
How to Jailbreak iOS 5.1.1 iPhone 4S Untethered With RedSn0w
Step 1: make a folder from your desktop and name it Pwnage.
Step 2: Now download the latest Redsn0w's version for Mac here, then put the Redsn0w within the Pwnage folder you created on step 1. And you can also download iOS 5.1.1 firmware here, however if you already downloaded the firmware or already on iOS 5.1.1,you can skip this phase.
Step 3: Now double-click on Redsn0w zip file to unzip it.
Step 4: (Skip this phase if your iOS is already on iOS 5.1.1) Connect your device to computer and then launch iTunes. Now choose your device's model appears on the device's list on the left side. And then hold down Option to click the Restore button. Restore is preferred as it won't create any wasted space on your iPhone.
Step 5: Now open Pwnage folder (from step 1) and then choose the iOS 5.1.1 firmware ipsw. Then hit Choose button in order to continue the step.
You should see now that your device is updated to the new firmware by iTunes.
Step 6: Now execute or launch Redsn0w from the redsn0w folder you unzipped previously on step 3.
Step 7: Now click Jailbreak button, once Redsn0w is launched.
Step 8: Well you will see the magic, the Rocky Racoon jailbreak will take three steps consecutively which are preparing, processing and then finishing up. Just wait until all the steps are entirely finished.
Step 9: When Redsn0w is complete with the three steps above. You will see your iPhone 4s takes reboot, when it finishes rebooting, you should see a new and fresh Cydia icon appears on your homescreen.
For Windows users: Untethered jailbreak iOS 5.1.1 iPhone 4s using Redsn0w 0.9.12b1 for Windows.