When you are signed in to Skype, the Skype logo is displayed in the Windows taskbar. You can also see your Skype status icon displayed in the system tray at the bottom of your screen.
If you close the Skype window, the Skype logo and status icon still appear in both the Windows taskbar and the system tray.
To remove Skype from both the Windows taskbar and the system tray, right click the status icon in the system tray and select Quit. This completely closes the application and signs you out, which means you will no longer receive instant messages or calls through Skype.
You can change your settings so that Skype is removed from the Windows taskbar when you close the application window by clicking X. This doesn’t sign you out, so you can still receive calls and instant messages while Skype runs in the background. You will still receive notifications for any IMs you receive in the system tray.
To do this:
Now every time you close the application window, Skype should no longer display in the Windows taskbar. If it does, then you may have to change the program properties. To do this: