MySQL Order before Group by

I need to find the latest post for each author and then group the results so I only a single latest post for each author.

SELECT wp_posts.* FROM wp_posts
        WHERE wp_posts.post_status='publish'
        AND wp_posts.post_type='post'
        GROUP BY wp_posts.post_author           
        ORDER BY wp_posts.post_date DESC

This is correctly grouping the output so I only get one post per author, but it is ordering the results after they have been grouped and not before they have been selected.