Everyone has their own reasons for wanting their phone to be untraceable, but traditional methods of hiding your phone number, like dialing "*67" before the call, will only disguise your caller ID number. Your ANI (automatic number identification) is still sent out, and can be traced if the person/company you're calling subscribes to this service. To make a call truly untraceable, you have to get a certain type of phone and take certain precautionary measures when using it.
Buy a GSM network prepaid phone from an electronics store. If you're unsure whether the phone is GSM or not, ask the customer service representative.
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Activate your phone by calling the number found in the instruction manual that came with it. Don't give your name or address when activating the phone. This will only lead a trail back to you when someone tries to trace your calls.
Make your calls short, and make them away from your home or regular hangout spot. Although the phone can't be triangulated (when a network service provider uses satellites and cell phone towers to pinpoint your approximate location) when it's turned off, it can be triangulated when it's turned on.
Remove the phone's SIM card (usually found underneath the battery) when you're done with it. This will ensure that your personal information won't get into the wrong hands when you throw the phone away.
Dispose of the phone after several uses. Prepaid phones are aptly nicknamed "disposable phones" for a couple reasons: they're cheap, and many people choose to get rid of them fairly quickly.