I want to organize my public_html/ folder so I want to move all files and folders of my forum script that are in there to a new folder (e.g. public_html/new). The question is how do I do that if I don't want to change the URL address?

To explain with other words, now I have:
public_html/page.html, URL: domain.com/page.html

and I want to have:
public_html/new/page.html, URL: same as above

Basically, like add-on domains or sub-domains work. The problem is that domain.com is my primary domain.