Upgrading Ubuntu 14.04 to 16.04 inside of Docker

I currently have a Docker image that uses another image as its base, and that base image uses Ubuntu 14.04. However, this Ubuntu version is out of date, and I would like to upgrade to the latest version of Ubuntu from inside my Docker image. Is there a way to edit my Dockerfile so that when I build my image, it updates the OS from 14.04 to 16.04? Thanks.