from your brief post i think i've got the jist of what your trying to do.
When you created your site in FP you probably gave the index page a title. This is generally carried through all the pages of the site and displays in the title bar,
If you then create an external link which opens in the same frame (current window) it too takes the same title as that through out your site.
I am not sure how you are displaying the link which takes people away from your site but if it helps you could just change the title on the page that is home to this link (if that makes any sense)
In FP, open the page that is home to the link (google as you earlier stated)
click on code view, if you look at the very top of the code, possibly about 7th or 8th line down you will see "Title" this will be the title that is displayed throughout the site. You can change this for that page only. That way when the external link opens it will not have your original title at the top.
Generally speaking, I think it is better to open an external link in a new window keeping yours in the background. When the viewer closes the other pages they might just take another look around yours.