For the modern version on Windows 10, you need to launch the app and go to Settings > General and turn on the “On close, keep Skype running” switch.Īnother annoyance you might have noticed is that when you right-click the Skype icon and select Close, it doesn’t remove the icon from the taskbar. Here’s how to get rid of the Skype icon without quitting it.
Update: This article was originally written for an old version of Skype.