Can each blog in WP Multisite have its own domain?

If I set up a network and define the main blog as http://www.mysite.com, I know I can set up the other blogs in the network to be:

http://www.mysite.com/site2
http://www.mysite.com/site3
http://www.mysite.com/site4

However, I want each blog in my network to appear as a completely separate entity to the end user, so I don’t want http://www.mysite.com to be in every domain. Can I set it up so each blog has a unique domain? I know when GoDaddy forwards a domain with mapping, it masks the home page, but then clicking any internal links shows the actual URL. I don’t want that. I want to set up my other blogs like:

http://www.site2.com
http://www.site3.com
http://www.site4.com

…and I want the content for each site to show accordingly. So if I click “About” on Site 3, it should look like this:

GOOD: http://www.site3.com/about

BAD: http://www.mysite.com/site3/about

Can I do this?

Thanks! 🙂