This tutorial assumes you already have your FTP manager open and are connected to your server
1) Browse to the directory where you installed Joomla

2) Right click the folder and select Rename
 
3) Type a new name for your Joomla directory and press Enter

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Now we need to update the configuration.php file with the changes
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4) Open your Joomla directory

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Scroll down
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5) Right click the file
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If you have a PHP editor installed, you can click View / Edit to automatically open the file with your default editor

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Otherwise, you will need to save the file to your computer and open it with a text editing program such as Notepad. We will do the latter
6) Click Download
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7) Now go to the location where you saved the file. In this case, it is the desktop

8) Right click the file

9) Go to Open With and choose Notepad

10) Find var $live_site and change the link to match Joomla's new location

11) Make sure to save your file

12) Return to your FTP manager
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13) Click and drag the file into your Joomla directory

14) With Overwrite selected, click OK
 
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That's it! You now know how to change the Joomla directory using an FTP manager and update the configuration file