Reach Joomla web site pages without directory name inside the URL

My server is hosting a Joomla website using this directories structure:

.
├── public_html
|   ├── wwwsite
|   |      ├── administrator
|   |      ├── bin
|   |      ├── cache
|   |      ├── ....
|   |      ├── .htaccess(**)
|   └── .htaccess(*)
├── ....

wwwsite: Joomla web site
.htaccess(*): inside this file I wrote the following Redirect rules to reach my website without the /wwwsite/ path.

Options +FollowSymLinks
RewriteBase /
RewriteEngine On
RewriteCond %{REQUEST_URI} !(\.|/$)
RewriteRule (.*) http://www.MYWEBSITE.com/$1/ [R=301,L]
RewriteCond %{REQUEST_URI} !^/wwwsite
RewriteRule ^(.*)$ wwwsite/$1 [L]

This configuration works correctly, so using www.MYWEBSITE.COM url, the index page of my Joomla site will be loaded correctly.
But if i navigate in my web site, every link of my index has the following url structure: ./wwwsite/index.php/.... instead of ./index.php/.... .
I tried to modify the second .htaccess(**) file with the following Redirect rules, but it doesn't work:

SetEnv DEFAULT_PHP_VERSION 5 
##
# @version $Id: htaccess.txt 9975 2008-01-30 17:02:11Z ircmaxell $
# @package Joomla
# @copyright Copyright (C) 2005 - 2008 Open Source Matters. All rights reserved.
# @license http://www.gnu.org/copyleft/gpl.html GNU/GPL
# Joomla! is Free Software
##


#####################################################
#  READ THIS COMPLETELY IF YOU CHOOSE TO USE THIS FILE
#
# The line just below this section: 'Options +FollowSymLinks' may cause problems
# with some server configurations.  It is required for use of mod_rewrite, but may already
# be set by your server administrator in a way that dissallows changing it in
# your .htaccess file.  If using it causes your server to error out, comment it out (add # to
# beginning of line), reload your site in your browser and test your sef url's.  If they work,
# it has been set by your server administrator and you do not need it set here.
#
#####################################################


##  Can be commented out if causes errors, see notes above.
Options +FollowSymLinks

#
#  mod_rewrite in use

RewriteEngine On


#  Uncomment following line if your webserver's URL
#  is not directly related to physical file paths.
#  Update Your Joomla! Directory (just / for root)

RewriteBase /wwwsite/


########## Begin - Joomla! core SEF Section
#
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteCond %{REQUEST_URI} !^/index.php
RewriteCond %{REQUEST_URI} (/|\.php|\.html|\.htm|\.feed|\.pdf|\.raw|/[^.]*)$  [NC]
RewriteRule (.*) index.php
RewriteRule .* - [E=HTTP_AUTHORIZATION:%{HTTP:Authorization},L]
#
########## End - Joomla! core SEF Section


########## Begin - Rewrite rules to block out some common exploits
## If you experience problems on your site block out the operations listed below
## This attempts to block the most common type of exploit `attempts` to Joomla!
#
# Block out any script trying to set a mosConfig value through the URL
RewriteCond %{QUERY_STRING} mosConfig_[a-zA-Z_]{1,21}(=|\%3D) [OR]
# Block out any script trying to base64_encode crap to send via URL
RewriteCond %{QUERY_STRING} base64_encode.*\(.*\) [OR]
# Block out any script that includes a <script> tag in URL
RewriteCond %{QUERY_STRING} (\<|%3C).*script.*(\>|%3E) [NC,OR]
# Block out any script trying to set a PHP GLOBALS variable via URL
RewriteCond %{QUERY_STRING} GLOBALS(=|\[|\%[0-9A-Z]{0,2}) [OR]
# Block out any script trying to modify a _REQUEST variable via URL
RewriteCond %{QUERY_STRING} _REQUEST(=|\[|\%[0-9A-Z]{0,2})
# Send all blocked request to homepage with 403 Forbidden error!
RewriteRule ^(.*)$ index.php [F,L]
#
########## End - Rewrite rules to block out some common exploits

What is my mistake?

[RESOLVED]

The .htaccess(**) file is not necessary. I resolved directly in configuration.php file of the Joomla web site, just setting the $live_site variable from public $live_site = ''; to public $live_site = 'http://www.MYWEBSITE.com';.

Now all links are correct!