A new method for the temperature-compensation of fundamental-mode orthogonal fluxgates that does not require additional hardware has been proposed and implemented. The method is based on the employment of one of the two fluxgate transfer characteristics and the phase of the corresponding output signal. The measurement according to the proposed method can be done during a single, unipolar cycle of the fluxgate excitation. This doubles the measurement update rate compared to conventional methods. The proposed method reduces temperature-drift errors by an order of magnitude. The fluxgate prototype has demonstrated a 20-fold (down to 100 ppm/degC) reduction of the temperature-drift errors