This modified version of BlackSn0w only works for phones upgraded with PwnageTool or Sn0wbreeze. Those who have updated to OS 3.1.3 by any other method will have the 05.12.01 baseband.
According to iHackintosh, the updated unlock also fixes a small bug that appears to make WiFi much more stable.
Blacksn0w RC2 will be available on MMI repo soon; however, you can add the source http://cydia.pushfix.info/ to Cydia and install it now.
Warning : Blacksn0w for 3.1.3 is still in RC stage and there may be some issues or bugs, for example, if you are faking your OS version to be 3.1.3 and you install the 3.1.3 version of blacksn0w RC2 with 3.1.2 CommCenter, you will cause problems! Your cell and WiFi could be unresponsive until you either uninstalled the package again via Cydia or restored the phone.
*Please note: this is not an official update performed by Geohot. He has indicated he will not be updating any tools for the 3.1.3 firmware.
Read More [via iSpazio]