If you have already updated your iphone 4 to ios 6.1.3 either knowingly or mistakenly it is obvious that now you don’t have more options to jailbreak iPhone 4. There is only one iphone 4 jailbreak available which is semi tethered which means you will need to boot tethered every time you need to reboot you must use your computer and redsn0w otherwise 6.1.3 Cydia will not work, in addition Safari will also crash.
You can also jailbreak iphone 3gs and ipod touch 4g using below jailbreak method.
How To Jailbreak iPhone 4 On iOS 6.1.3
Step 1: Download Redsn0w 0.9.15b3 from our jailbreak download page, extract and run as administrator. Also download iOS 6.0 firmware file specific to your iphone 4 from our iOS download page.
Step 2: Connect your iPhone4 to computer and on main redsn0w window go to Extras => Select IPSW => Now browse and select the ipsw file which you downloaded in step 1.
Step 3: After selecting 6.0 ipsw go back to main menu and click Jailbreak => Click Continue => Select Install Cydia => Put your iphone 4 in DFU mode and let the jailbreak process to complete.
Although the iphone 4 is now jailbroken but it requires tethered boot so that you can be able to use Safari and Cydia otherwise these two apps will not work.
Install Cydia After iOS 6.1.3 iPhone 4 Jailbreak
If you have jailbroken your iphone 4 using redsn0w for 6.1.3, you will not see Cydia after 6.1.3 jailbreak. Since this is a semi tethered jailbreak iphone 4 for iOS 6.1.3 you will require to boot tethered by following below step to install cydia.
Boot Tethered After jailbreaking iPhone 4
From main Redsn0w window go to Extras => Select IPSW => Browse and select 6.0 ipsw as we did in step 2. Go back to Extras and click Just boot, just complete the process and put your device in DFU mode. After this step is complete your iphone 4 is now jailbroken on iOS 6.1.3.