This paper addresses a still unknown effect of a high downward gradient of the square of the magnetic flux density on a laminar methane diffusion flame established over an axisymmetric co-flow burner. Because the magnetic force is expected to act mainly on paramagnetic oxygen, a parametric study varying the co-flowing stream oxygen content, the oxidizer velocity and the magnitude of the gradient of the square of the magnetic flux density was performed. CH* radicals spontaneous chemiluminescence was captured to track the flame sheets. Despite a low Reynolds number at the fuel exit and oxidizer flow velocities slightly larger than the fuel exit velocity, the flame flickering was triggered by downward gradients of the square of the magnetic flux density of magnitudes from 0.4 and 1.4 T-2/m for O-2 contents of 0.75 and 0.55, respectively. This flickering is shown to result from an axisymmetric mode of a convective instability. Qualitative speculations based on previous works suggest that the magnetic body force may alternately strengthen buoyancy and shear stress, therefore hastening the instability onset. Indeed, at relatively low Grashof numbers, a region of flickering conditions shows up and grows with a magnetic Reynolds number. The sensitivities of the flickering frequency and amplitude are finally addressed, namely showing that over the investigated range of parameters the frequency spreads from 10.5 to 14 Hz. (C) 2010 The Combustion Institute. Published by Elsevier Inc. All rights reserved.