When we disable these suggestions, Google saves a cookie on your computer to remember that suggestions have not to be shown. But, if you choose to clear all cookies when Firefox closes from Options for privacy and security, then these suggestions start re-appearing. To remove Google search suggestions permanently you need to add cookie exceptions so that they won’t get deleted once you close Firefox.
The first thing you need to do is to disable search suggestions from settings page.
Then, you need to add cookie exception by going to Tools > Options > Privacy Tab. Click on exceptions button and then add following filter so that Firefox never deletes Google setting cookies. http://.google./complete/search?*
To remove search suggestions from Google search box present beside address bar, follow the below steps:
Enter about:config in Firefox address bar and press enter. Accept the warning.
Search for browser.search.suggest.enabled
Double Click on it to set its value as false. Restart Firefox and now you will not find any suggestions in search box, irrespective of search engine or settings.