How do I reconnect HTTP to HTTPS with subdomain?

Question

I have the following HTTP address:

http://www.example.com/

but my HTTPS address has a subdomain and no www, like this:

https://secure.example.com/

---

I tried the following rule:

<IfModule mod_rewrite.c>
RewriteEngine On
RewriteCond %{HTTPS} off
RewriteRule ^(.*)$ https://secure.%{HTTP_HOST}%{REQUEST_URI} [L,R=301]
</IfModule>

Which sent me to:

https://secure.www.example.com/

---

How can I force HTTPS in this situation? As I need the www removed.

---

EDIT: I have these rules above them for 'fancy urls' as I'm using WordPress as CMS:

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

Answer 1

This should be your complete htaccess :

RewriteEngine On
RewriteBase /
#1--Redirect "http://domain to "https://secure"
RewriteCond %{HTTP_HOST} ^(www\.)?domain\.com$
RewriteCond %{HTTPS} off
RewriteRule ^(.*)$ https://secure.domain.com%{REQUEST_URI} [L,R=301]

#2--wp rules--#
RewriteRule ^index\.php$ - [L]
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule . /index.php [L]

Answer 2

<IfModule mod_rewrite.c>
RewriteEngine On
RewriteCond %{HTTPS} off
RewriteRule ^(.*)$ https://secure.example.com/$1 [L,R=301]
</IfModule>

OR

RewriteCond %{SERVER_PORT} 80
RewriteRule ^(.*)$ https://secure.example.com/$1 [R=301,L]

Both rules do exactly this: any non-https request is redirected to https://secure.example.com while preserving the whole url