Get last updated time for all items grouped by category

Get last updated time for all items grouped by category

here is my table of items:
id (int)
category_id (int)
title (varchar 255)
updated_timestamp (int)
Each item has a category_id. Let's say I have this data:
1 | 14 | item 1 | 1376164492
2 | 11 | item 2 | 1376164508
3 | 12 | item 3 | 1376164512
4 | 14 | item 4 | 1376164532
5 | 12 | item 5 | 1376164542
6 | 11 | item 6 | 1376164552
My goal is to get last update timestamp for each category. As a result I
need this:
11 = 1376164522 (greatest value for all items with category_id = 11)
12 = 1376164542 (greatest value for all items with category_id = 12)
14 = 1376164532 (greatest value for all items with category_id = 14)
Here is my SQL:
SELECT
`category_id`, `updated_timestamp`
FROM
`my_table`
GROUP BY
`category_id`
ORDER BY
`updated_timestamp`
DESC
But when I run it I have a result like this:
11 = 1376164508 (lowest value for all items with category_id = 11)
12 = 1376164512 (greatest value for all items with category_id = 12)
14 = 1376164492 (greatest value for all items with category_id = 14)
Another words, DESC does not work. What I am doing wrong?
Thank you!