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To discontinue Twitter, visit Twitter.com and log in to your account. Once you’re signed in, locate the settings menu—represented by a gear icon—and click it. Next, chooseSettings from the menu, and on the resulting page scroll to the bottom and selectDeactivate my account. Twitter will ask you to confirm that you really want to deactivate your account. If you do, click the Deactivate button, and don’t ever return to Twitter again.
When you deactivate the Twitter account, Twitter will remove your profile and tweets from the site, and if someone tries to view your profile page, they’ll get a message saying that your account doesn’t exist.
If you feel remorse after deactivating your account, you have 30 days to change your mind: Twitter will retain your account and user data for that period, and all you need to do to reactivate your account is to visit Twitter.com and log in with your username and password. So if you want to delete the account never login to Twitter within 30 days after the deactivation.