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Orthogonal fluxgate in fundamental mode has become a competitive sensor for low noise measurement of low frequency magnetic fields. The noise of this sensor has been recently reduced to 2.8 pT/√Hz at 1 Hz; however, it appears that noise lower than 2.5 pT/√Hz at 1 Hz cannot be achieved because of the physical limitations due to the intrinsic noise generated in the core of the fluxgate. In order to decrease the noise below 2.5 pT/√Hz at 1 Hz, Barkhausen noise generated in the core must be reduced. For this purpose, we annealed the amorphous wire used as the core of the sensor in an infrared furnace while a dc current was flowing through the wire. The dc current generated a circumferential field large enough to saturate the wire in a circumferential direction, and by annealing the saturated wire, we increased the circumferential anisotropy. We illustrate the dependence of circumferential anisotropy on dc current in the wire as well as on temperature and time of annealing. We then demonstrate that larger circumferential anisotropy helps reduce the noise of the sensor suppressing the Barkhausen noise when the fluxgate is operated in fundamental mode. As a result, a 1.8 pT/√Hz noise at 1 Hz was achieved with annealed wire, which is far below the 2.5 pT/√Hz minimum noise achievable for sensors with as-cast wires.