Quit Skype by selecting Skype > Quit Skype.
Open your Applications folder and drag your copy of Skype to the trash.
Then open ~/Library/Application Support * and drag the Skype folder to the trash. The ~ sign represents your home folder. To find your home folder, open Finder and, from the menu bar, select Go > Home.
Important: If you’d like to keep your chat and call history, skip this step.
Open ~/Library/Preferences and drag com.skype.skype.plist to the trash.
Open Finder and search for “Skype” using the search feature in Mac OS X. Move all of the results returned to the trash.
Click Ctrl and the trash icon, and select Empty Trash.
Restart your computer.