How can I change the page URL without refreshing the page?

How do I change the URL without refreshing the page?

I've built a website with CodeIginer and I want to implement AJAX and JQuery in one of my pages. The problem is; when I load the content, the URL doesn't change.

Let's say that I have the URL http://www.example.com/controller/function/param
And another URL : http://www.example.com/controller/function/param2