How can I remove the Ethernet icon from the task bar

I have 2 items in Network Connections of my XP. One is the Gigabit Ethernet Controller and the other is the Wireless Adapter. I connect to the Internet only through the Wireless Adapter. I have been connected to the Internet almost the whole day for the last one week and the adapter is working fine, and the icon is displayed on the Task bar as it should.

The icon for the Ethernet Controller is also on the task bar with a red cross on it because it is not used for the internet. How can I remove this redundant icon from the Task bar?