Unpinned taskbar icons moving around the taskbar

My problem is specific to the unpinned icons in Windows 7 Home Edition 64-bit. The pinned applications stay put just fine. This problem started a couple of days ago.

It seems that, when I have multiple unpinned applications open, sometimes the icons of the unpinned applications move around at random times (it seems that the last active unpinned application moves to the right even though it wasn't the program opened last). And sometimes, when I have only one unpinned application on the taskbar, its icon seems to move from some slot to its right back in its position.

For some reason I suspect some malware or virus may be the cause.

I tried uninstalling ATI Radeon HD6450 drivers and reverting to an older version, as well as uninstalling every program that was installed since the day the problem started, to no avail. I found four malware in the meantime but even removing said malware did not solve my problem.