Some users ask for a fix for a double redirect. But Really Simple SSL does not do a double redirect!
But you want your double redirect fixed, right?
You should check your .htaccess and other plugins carefully. Some caching plugins and security plugins also handle redirects to https, and maybe you or someone else added a redirect to the .htaccess independently of this plugin.
- Backup your .htaccess file and remove all rules concerning https that are not generated by Really Simple SSL, and check again.
- Deactivate your plugins one by one, clear your cache, and check again.