The current ATI catalyst driver does not install on Fedora 20. I needs to patched in order to be installed successfully. Here are the how to instructions for building the beta ATI driver for the following:

OS: Fedora release 20 (Heisenbug)
Architecture: x86_64 (64-bit)
X Server: XServer 1.14.4
Kernel: 3.16.2-200.fc20.x86_64 #1 SMP Mon Sep 8 11:54:45 UTC 2014 x86_64 x86_64 x86_64 GNU/Linu

Make sure your kernel devel and headers are installed:
yum install kernel-devel kernel-headers

Next download the latest ATI driver:
cd /tmp
wget –referer=http://support.amd.com http://www2.ati.com/drivers/beta/linux-amd-catalyst-14.6-beta-v1.0-jul11.zip

Now unzip and extract the run binary:
unzip linux-amd-catalyst-14.6-beta-v1.0-jul11.zip
cd fglrx-14.20/
./amd-driver-installer-14.20-x86.x86_64.run –extract patched

Once the run binary is extracted, we need to download and patch firegl_public.c:
cd /tmp/fglrx-14.20/patched/common/lib/modules/fglrx/build_mod
wget http://devgurus.amd.com/servlet/JiveServlet/download/1304255-7665/firegl_public_c.patch.zip
unzip firegl_public_c.patch.zip
patch -u < firegl_public_c.patch Once the firegl_public.c is patched, then run the following to make it as root or using sudo:
./make.sh

Once built, go to the following directory and install everything:
cd /lib/modules/fglrx
make install

Everything should successfully install. Reboot and enjoy a working desktop. Remember, run the following to bring up the catalyst configuration tool:
amdcccle