We have found parameters of the box-shaped lens with the low aberration level. A method of phase diagrams was used for analysis of lens properties and creation of an algorithm of iteration procedures. Linearity of transformation of lens trajectories is achieved by varying parameters of elliptic gaps between electrodes and values of electrode potentials. At a lens outlet, a linearly-formed beam has a width of 40 mm and a phase diagram shaped as a rectangle 40 mm x 0.1 mrad. Keywords: ion optics, emittance, lenses, phase diagrams, aberrations