Hi Fanny,
Not sure whether this will help. You may have a "Filtered Item List" Includelet on the page with the sub-menu. When you go to "Edit this page" have you looked at the Layout tab (between "Edit" and "Relations")? The Layout tab should include the "Content" Includelet as standard (don't delete this), but below the Content Includelet is there another Includelet called "Filtered Item List? If there is, it is this that is probably generating the menu that you want to remove. Having a left-hand menu is sometimes useful as it lets users know that there are other pages below - I have used therm on a few pages within my website.
You can always scratch the Includelet and if it works - all well and good. If it hasn't worked or if it has and you want to re-instate the menu then you can drag it back to the "Content".
Hope this is of some help.
Alan Parry