Google Desktop Bar? Did I Miss something?

Well, started my PC this morning (yes, there´s still some need for it) and was astonished about a small „Google-search-tool-something“ on the upper right corner of the Desktop. Yes, I recently installed Googles Desktop search there, but I´ve never noticed this search tool – one can even drop it into the taskbar – but where does it come from? Did Google install it? Did I want them to? I can´t remember though I´ve to admit that an employee used my PC yesterday – I´ve to do some research to find out if she noticed it…If not, I think this is a „no-go“ behaviour of Google, just installing and doing what they want on my Desktop…