WordPress in a directory, redirection problem

My WordPress is installed in a subdirectory, so I have http://www.mywebsite.com/mydirectory. Everything works find, I change the index.php, the line in the settings, etc. and my website is now viewable at http://www.mywebsite.com. My problem is that when I type http://www.mywebsite.com/wp-admin, I’m redirected to http://www.mywebsite.com/mydirectory/wp-admin… and it’s stupid because that’s why I installed my WordPress in a directory –‘

I’m 90% sure it’s the .htaccess, so here is the code:

# BEGIN WordPress
<IfModule mod_rewrite.c>
RewriteEngine On
RewriteBase /
RewriteRule ^index\.php$ - [L]
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule . /index.php [L]
</IfModule>
# END WordPress