domain alias with base_url

Supposed I install CI in site: subdomain.maindomain.com which I have base_url subdomain.maindomain.com
I also rent domain call www.otherdomain.com which is an alias for subdomain.maindomain.com.

When I go to www.otherdomain.com, It will open subdomain.maindomain.com. So how to keep base_url to www.otherdomain.com when
I use that domain for browsing?

I mean to make 2 domains looks as separate domain.