We present a new method for directly determining accurate, self-consistent cluster lens mass and shear maps in the strong lensing regime from the magnification bias of background galaxies. The method relies upon pixellisation of the surface mass density distribution which allows us to write down a simple, solvable set of equations. We also show how pixellisation can be applied to methods of mass determination from measurements of shear and present a simplified method of application. The method is demonstrated with cluster models and applied to magnification data from the lensing cluster Abell 1689.

5 pages, 4 figures. References added to introduction. Accepted by MNRAS