This is a function of your internet browser, and does not rely on your internet history.
Please be aware there is another function on most browsers (not related to your history) called Auto Complete. This is not based on the web history of your specific computer, but rather based on searches by other users which began with the same letters. For instance, if you go to www.google.com and type the words "How to cook" google will suggest many ways to end the sentence (How to cook rice, how to cook turkey, etc.). These suggestions are based on what past users have searched for after typing the letters "how to cook."
You can find instructions on how to disable this feature in Internet Explorer by following this link.
You can find instructions on how to disable this feature in FireFox by following this link.