Updated: I have renewed all links for the patch. If you still have problem with the link, do not hesitate to contact me. Thank you for all you that have informed me about this link problem.
Again, we need to patch the source code of fglrx kernel module, part of ATI Catalyst (you will find it on /lib/modules/fglrx after installation), for kernel 2.6.39.x since there are some changes on the kernel. On this post, I will show how to patch ATI Catalyst 11.x (tested on 11.5) and 10.10 - 10.12 (tested on 10.12) so that it works on 2.6.39.x (tested on 220.127.116.11).
ATI Catalyst 11.x
First, download 2 files: 2.6.39_bkl.patch and no_bkl.patch (Thank's to https://aur.archlinux.org/packages.php?ID=41040 and http://www.mindwerks.net/2011/04/ubuntu-11-04-natty-with-fglrx-and-2-6-39). Copy those files to /lib/modules/fglrx/build_mod then run these commands:
patch -p1 < 2.6.39_bkl.patch
patch -p1 < no_bkl.patchNext step, execute ./make.sh and if there is no error, change directory to /lib/modules/fglrx then execute ./make_install.sh
ATI Catalyst 10.10 - 10.12
You have to download this patch: fglrx_10.10-12_with_2.6.39.x.patch. Copy this file to /lib/modules/fglrx/build_mod then execute:
patch -p1 < fglrx_10.10-12_with_2.6.39.x.patch
After that, execute ./make.sh and if there is no error, change current working directory to /lib/modules/fglrx then execute ./make_install.sh
Note: for my other posts about ATI Catalyst, go to this link. You may need to read it.