Just open your Skype Client, Click on tab "Skype" and Select "Account" from the menu, then your browser will open web interface of your Skype Account, Log in there and look for the Link "Account settings" under "Account details"
Click on "Account settings", a new page will come up.
Look for section "Linked accounts" and you will find a link that shows "Facebook account: Linked ". Here, Click on "Unlink" and a new box will pop-up.
Confirm pressing "Continue" and you are all done there, your Facebook Account will be unlinked from your Skype.
Have a look at the attached Image, it shows the total procedure in 4 easy steps.
