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To securely delete a file:

1. Add the file to the Trash Bin. 
2. Choose Finder from the menu bar.
3. Click "Secure Empty Trash..." When you do this, not only is the file removed from the Mac’s directory, but the hard drive space it occupied is overwritten with random binary digits.

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You may also adjust your settings so that files are removed securely each time you empty the trash. To adjust this setting:

1. Click Finder from the Menu Bar.
2. Select Preferences.
3. Click Advanced. 
4. Check the box to "Empty Trash securely."