Search Cleanup Question

I am using the latest Firefox Quantum software on my laptop with Windows 7 OS. I am wondering why, after running the CCleaner software, when I start typing a site in the URL window, do past sites show up as suggestions? I can't help but wonder if Google has planted a file in my computer that CCleaner does not clean up. This does not occur when I use my iPad.

Does anyone have any idea as to why this is occurring and how I can prevent this from occurring?

 

I forgot to add, but I always start Firefox in privacy mode (new private window). Also, this occurs even after I clean up my browsing history.

 

I'm still using an older version of Firefox but it should be similar.
Open Options > Search and uncheck 'Provide search suggestions'.

 

Thanks, Eldon. I do not have the 'Provide search suggestions' box checked.

Also, on CCleaner, under the Options settings, under the Settings, Include, Exclude and Advanced tabs, I have unchecked all of the cookies and temp files settings for the program to remove everything. Yet I still see suggestions as I begin, but not finish, to type in web sites that I have been to previously. These suggested web sites are all sites I have been to previously.

 

Look at the settings of the search engine you use.

 

Remove the 3 ticks in the Address Bar.