After the firmware version 013.016 for N8, Nokia has released the same update for Nokia C6-01.
The 013.016 update brings performance and usability improvements as well as an enhanced social networking experience with more convenient picture and video sharing, a new version of Quick Office with a free editor’s license and a new version of Ovi Store. With the improved calendar, it is possible to respond to meeting requests and see the meeting location on the map.
To get this software through your device, select Applications > Software Update, and choose the software you want to update. Alternatively, this software release is available through the Nokia Ovi Suite.
For more safety you should make a backup of important data on your phone before to hit the update.