Allowing cross origin requests (CORS) on Nginx for 404 responses

I'm using Nginx to serve static files in response to CORS requests using the technique outlined in this question. However, when the file doesn't exist the 404 response does not contain the Access-Control-Allow-Origin: * header and so is block by the browser. How can I send Access-Control-Allow-Origin: * on 404 responses?

[kzm1760]

"more_set_header" なるほど