You are describing the Google browse by name feature which is the default behavior on Firefox 3.6

To get this behavior on Firefox 4 you need to change a hidden preference.

1. Type about:config into the location bar and press enter
2. Accept the warning message that appears, you will be taken to a list of preferences
3. Locate the preference keyword.URL, double-click on it and change its value to the link shown below

http://www.google.com/search?ie=UTF-8&oe=UTF-8&sourceid=navclient&gfns=1&q=

If you prefer, you can also do this by installing the Browse by Name extension - https://addons.mozilla.org/firefox/addon/browse-by-name

I did the changes and it worked really well. But when I opened a new window the problem was there again... Any solution on this problem?

This link may help - https://support.mozilla.com/kb/Preferences+are+not+saved

I didn´t have any file called user.js, so the problem is still there :-(

@TonyE thankyou for this fix, sorry it took so long to reply,, exam period and all that! @ST71 I had exact the same problem, mine kept reverting to AVG search, but it has now stopped. All I had to do was turn my laptop off, a very rare occurence, normally I put her to standby and come back in an hour to carry on. might be worth doing the fix as described, shutting down immediately after then rebooting, see if it holds. if its AVG like mine, check your add-ons, I've disabled some to make this stick.

good luck!