How to create the right internal redirect?

The essence of this is to do an internal redirection request site.ru/name_folder/ to load content from site.ru/myfolder/name_folder/. There are ready-made htaccess

RewriteCond %{REQUEST_URI} !^/index.html$
RewriteRule ^(.+)$ /myfolder/$1 [L]

It works, but when the requested page without the slash at the end site.ru/name_folder something moving to the page site.ru/myfolder/name_folder/, and it is necessary to stay on the page site.ru/name_folder/