This study shows that using the direct offset integration technique (DOIT) and additional positive feedback (APF) in a high-Tc dc superconducting quantum interference device (SQUID) improves the effective flux-to-voltage transfer function and reduces the flux noise of a magnetometer, thus improving the magnetic field noise. The effective flux-to-voltage transfer function and the flux noise with APF were measured at different values of the positive feedback parameter βa, which depends on the resistance of the APF circuit. These quantities were also compared between conditions with and without APF. This investigation showed that a βa condition the most suitable for minimizing the flux noise of a magnetometer with APF exists and that it is βa=0.77. The effective flux-to-voltage transfer function with APF is about three times what it is without APF (93 µV/Φ0 vs. 32 µV/Φ0). The magnetic field noise of a magnetometer with APF is improved by a factor of about 3 (242 fT/Hz vs. 738 fT/Hz).