Add extra fields to Add New Category page

Question

I need to add an extra field to the Add New Category page. Currently it only has fields for Name, Slug, and Description. Essentially, I need to have a second description text box.

I use the current Description field at the bottom of each category page, but now I need to have additional information specific to the category (and different from the bottom) displayed at the top.

How can I add this additional field?

Below is what I am trying to achieve:

Answer 1

If you want a plugin solution, advanced custom fields can do this.

Answer 2

Ended up solving this with bainternet's plugin at http://en.bainternet.info/2012/wordpress-taxonomies-extra-fields-the-easy-way