Influence of magnetic fields on the liftoff and blow out properties of the methane/air co-flow diffusion flame has been investigated experimentally. The present experiments showed that magnetic gradients are able to minimize the liftoff height and increase the flow rate above which the flame blows out. This observed increase of stability of lifted flames is attributed to the magnetic force that develops on paramagnetic oxygen in magnetic gradients. Two mechanisms are provided to explain the extension of the lifted flame stability. By decreasing locally the air velocity upstream of the flame, the magnetic force, resulting from an upward decreasing magnetic field, modifies the fuel mixture fraction at the flame edge, reducing the liftoff height of the flame. The second mechanism is related to the variation of the magnetic susceptibility with temperature and oxygen mass fraction in which originates a magnetic convection phenomenon in air in the flame vicinity.