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A method is proposed by which a magnetometer with symmetric response and zero offset can be realized with an orthogonal fluxgate. The sign of the sensitivity is changed by changing the sign of the dc bias current to the wire core of the magnetometer, whereas offset is unchanged. Symmetrical response is obtained by taking the difference of outputs obtained with a positive dc bias and with a negative dc bias, which also leads to zero offset. A prototype is examined with an as-cast amorphous Co-based wire as a core. Good performance is obtained with small excitation current (ac component 5 mA, dc component 7 mA).