Article: On Facebook, location services can only be disabled on a per-post basis. If using the mobile Facebook app, tap on the “pin” icon, then tap on the “X” next to your current city at the bottom of the cities list to remove your location.
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Log in to Facebook and write an update status. Click on the “pin” icon located at the bottom left corner of your post, then click on the “X” located to the right of your location.