apache - .htaccess redirect to external URL while hiding redirect

Question

I want to be able to redirect a domain pointed to my webhosting to an external domain.

For example, I have this in my .htaccess:

RewriteCond %{HTTP:Host} ^(?:www.)?mydomain.example$ 
RewriteRule ^(.*)$ http://myexternal.example/site [R=301,NC]

However, when I visit the domain, the URL in my address bar changes to http://myexternal.example/site.

How can I redirect without changing the URL?

Is there another way around this? Do I need to use a frame/iframe?

Answer 1

Bit long ago, but I'll answer the question anyway for those who come here by Google (like me). The answer is really simple:

In your htaccess, remove the R=301 part (and the comma of course).

R=301 means you do it via a 301 redirect. You don't want that