Office 2010, IE 9 - IE10, SharePoint Online (SPO O365), when a user clicks on a document in a SharePoint document library two instances of the office application are started. Two windows showing the same document are opened by the single click in the document library.
**This workaround does have some side effects, lose benefits of the trusted zone settings**
In Internet Explorer go to "Internet Options" screen, and select the "Security" tab.
Remove the SharePoint online address from the trusted sites list.
This is a known issue and is actively being looked at by the product groups right now.
The estimated sever side fix date is sometime in March.