For Fedora 24 and Fedora 23 and Fedora 22 (also 64 bit!).
Download Skype from: http://www.skype.com/en/download-skype/skype-for-computer/ and choose Fedora 32 bit (no 64 bit package available, but that doesn’t matter).
In my case it was version: skype-4.3.0.37-fedora.i586.rpm
Open terminal, go to
~/Downloads/
(or wherever you have put the file) and run:sudo dnf install skype-4.3.0.37-fedora.i586.rpm
and all the dependencies will be resolved automagically.
That is it!