wordpress 404 - una vez a 404 y una vez a la página de inicio

I have a problem with the 404 in my site. I didn't build the site, just fixing some issues there.

I'm using the default permalink structure, and have a 404.php in my theme folder. My .htaccess:

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

The problem is: when I change the URL to /?page_id="page number that doesn't exist" - I get the 404 page, but when I just write some letters (e.g. /sjkhdk) I get the home page (I want them both to get to the 404 page).

¿Alguna idea?

Gracias, Tal