Redirection from a directory with www to the same directory without www

I would like to make a permanent 301 redirection : fro开发者_运维问答m all the html files of example.com/directory/ to all the html files of www.example.com/directory/

Stolen from innumerable sites, after a quick google for "htaccess remove www",

RewriteEngine On 
RewriteCond %{HTTP_HOST} ^www.mysite.com$ [NC] 
RewriteRule ^(.*)$ http://mysite.com/$1 [R=301,L]