IMPORTANT: You can only unlink your accounts once – please ensure you want to do this before proceeding.
To unlink your Skype account from your Microsoft or Facebook accounts:
Sign into your account.
In the Settings and preferences section, click Account settings.
On the Account settings page, click Unlink next to your Microsoft or Facebook account.
If the account has Not linked as an option rather than Unlink, it means your Facebook or Microsoft account isn't currently linked to your Skype account. If you were expecting to see a linked account, ensure you've signed in with the correct Skype Name.
An information window opens. Read the information and, if you agree, select Continue to unlink your Skype and Microsoft or Facebook accounts.
If you sign in with a Microsoft account, unlinking will mean you can no longer sign into Skype with that Microsoft account (your Microsoft account will not be closed; only your access to Skype with that Microsoft account will be affected). Read the message that appears and, if you agree, select Close account.