Give this a try :

Type in the address bar   about:config   (press Enter) (promise to be careful, if asked) Type and look for the preference : browser.search.suggest.enabled and set it's value to   false

Note :   this goes for search results in the search bar only   - not for search results in the URL bar. For searches in the URL bar you'd have to change the preference : browser.urlbar.suggest.searches and set it's value to   false

Also :   (just to make sure that you haven't overlooked anything)   -   would you please go over the 'Table of contents,   in the article :

Use popular search suggestions in the Firefox Search bar

it was in false when I get to it.

the problem doesn't appear in the search bar of Firefox, it appears inside the search bar inside the website of Google.

I try it in Internet Explorer and the result is the same. it seem it lays on Google. thank you for your answer and your help.

If you are logged to Google when this happens then you may have enabled the History feature in the Google settings.

• https://www.google.com/preferences?hl=en&fg=1