Install the Skype repository. In the terminal, type:
gedit /etc/yum.repos.d/skype.repo
Copy and paste the following lines to the file
[skype]
name=Skype Repository
baseurl=http://download.skype.com/linux/repos/fedora/updates/i586/
enabled=1
gpgkey=http://www.skype.com/products/skype/linux/rpm-public-key.asc
gpgcheck=0
In the terminal, type:
yum install skype