It's not a bad implementation. There really is no "most effective" way to do tabs; just use whatever it takes to get the job done. If you don't feel like including a library like jQuery into your page, then that should work fine. Just test it and make sure that it works on all of the browsers.
However, using a library with a pre-built tabs implementation that has been tried and tested on many different browsers and platforms will probably fair better in the real world.