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I think he means a new url not a new web site..
I always change the url and keep the same content and then redirect any traffic to the old url to the new one at the server not on the page.
If you have a shared hosting you should be able to do this in your control panel other wise you will need to put in a redirect at the server level.
Whatever you do, don't use the meta tag version!
Don't employ cloaking or sneaky redirects
Meaning the meta refresh tag.
If you generally need to redirect this should be done at server level.
The meta refresh used to be seen as a trick so robots could crawl the content.
I am sure we had a discussion here on webmaster world that Google guy stated that redirects should be done at the server.
I would either delete the page, and update all inbound links, and use a custom 404 page that perhaps links to your home page or the site map.
If you really don't want to delete the page, put a page using the old file name that only has a link to the page's new location (don't duplicate the content) and use a meta refresh to redirect to the new page after a few seconds.
G will *not* punish you for this. After a couple of weeks, or days, when the new page is in the SERPs, delete the meta refresh page, and allow the old URL 404 as suggested above.