If you want to update Skype on your iPhone or iPod Touch to the latest version, you don’t need to uninstall Skype. When a newer version of Skype is available for your Apple device, simply visit the App Store to install an upgraded version.
Learn more about Skype for iPhone.
However, if you want to uninstall the older version of Skype for iPhone before installing the latest version, simply tap and hold the Skype icon on your home screen until the icon begins to shake and an x appears in the corner of the icon. Release the icon and then tap x. This will uninstall the application.
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