The viscous fingering instability of miscible shear-thinning fluids has been examined using a pseudo-spectral numerical technique based on the Hartley transform. The instability was studied for a flow in a rectilinear Hele-Shaw cell, and the shear-thinning character of the fluids has been modelled using the Carreau equation. New mechanisms of viscous fingering not previously observed in the case of similar Newtonian flow displacements have been identified. These mechanisms, which are reminiscent of the fractal patterns observed in experimental studies, were interpreted in terms of the velocity-dependent mobility of the flow.