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composer self-update
Chris
composer self-update
php composer.phar self-update
If going from version 1 to 2 use composer self-update --2
To update composer command just find location of composer.phar and update as:
where composer #Retrieves you location of your composer.phar
cd path_to_composer.phar #Move to directory with composer.phar
php composer.phar self-update #Update your composer