Go to System Preferences > Network.
Select Airport from the left hand pane
Click Advanced in the right hand pane
Click the Airport tab.
Select the Network Name that you want to get rid of and click the "minus" button.
Your airport looks for your old one first because it is at the top of the list.
The above works with 10.5 for sure. Should work for all OS X but with slight variations
P
I was having a problem with my Airport Extreme Base Station so I reset it and set up a new network. I also have an Airport Express. My wireless network is working fine now except for one annoying thing. The old network name that doesn't exist anymore always shows up under the Airport bars and sometimes it's the first network my airport looks for so I have to manually change it. How do I get rid of it?

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