  We develop an algorithm for the reconstruction of the two-dimensional mass
distribution of a gravitational lens from the observable distortion of
background galaxies. From the measured reduced shear, the lens mapping is
obtained, from which a mass distribution is derived. This is unlike other
methods where the convergence ("kappa") is directly obtained. We show that this
method works best for sub-critical lenses, but can be applied to a critical
lens away from the critical lines. For finite fields the usual mass-sheet
degeneracy is shown to exist in this method as well. We show that the algorithm
reproduces the mass distribution within acceptable limits when applied to
simulated noisy data.
