Nintendo released a statement warning customers to cease usage of the Nintendo Wi-Fi USB Connector. The statement warns against potential viral attack.
Nintendo tweeted the information out on their official Japanese account, as first noticed by GoNintendo and more extensively written up by Nintendo Life. The peripheral was released back in 2005, and Japan got an exclusive version, called the Wi-Fi Network Adapter, in 2008. In those bygone times, Wi-Fi was not as common as it is today. The USB Connector plugged into a PC connected to broadband and allowed Nintendo devices to have access to the network. Those without Wi-Fi could, with a little extra cash, connect their devices and enjoy online features.
Clearly, Nintendo has concerns that the device is a security threat or liability and encourages users to cease usage and switch to a different network device. You may also not have a good reason to keep your Wii or DS online in the first place. The Wii Shop Channel shut down back in January 2019. For several months in 2022, Wii users couldn't download past purchases, though the feature quietly returned.
These devices last shipped out in 2010, for the Connecter, and 2013, for the Adapter. So the chances that you are still using the device to connect your Wii or DS to Wi-Fi is probably slim. However, if you are, it's probably best to heed Nintendo's advice.
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