http://bit.ly/1KIFuKV Using Local Group Policy Editor in Microsoft Windows 10, it is possible to completely disable Cortana, without it restarting, and without editing the registry, or making forced changes. #cortana #windows10
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Additional notes 2015-11-15:
It is true that this process disabled Cortana, but does not remove the process. This is still an effort that people are working on and discussing. If you wish to join in further on that discussion, we have an open thread at https://windowsforum.com/threads/how-to-properly-disable-cortana-in-microsoft-windows-10.211998 for this issue.
If you do not have Windows 10 Pro and are using Home or Core edition, you will not have access to Local Group Policy. For those users, this solution will not work at all. FYI.