Note: For the Skype for Linux stable version go to the below link
Recently microsoft has released Skype for Linux Alpha version of a Skype Web app for Linux.This alpha version of Skype for Linux is a brand new client using WebRTC technology.Using this new skype version, you will be able to call on the latest versions of Skype on Windows, Mac, iOS and Android.
Install Skype for Linux Alpha
Go to the Skype for Linux Alpha download page and and click the Download Skype for Linux Alpha DEB button to download the the latest version of Skype for Linux Alpha in .deb file. The downloaded file size is around 41MB.
Double click the downloaded .deb file. It will open the Ubuntu software center. Just click the install button and type your ubuntu password. You can also install it via GDebi package manager.
After the successful installation restart ubuntu and click the Dash home from unity launcher. And type Skype for Linux Alpha in the search field.Then click Skype for Linux Alpha to open it.