In this paper, a robust multi-pass printing method is introduced. This is a technique where a new design variable is included: a weight factor A(n) that affects the density of dots being printed by every nozzle in the print-head. In the paper, the dot density of a vertical multi-pass system is described in an analytical expression. Then, it is theoretically shown how the minimization of the roughness measure of above expression with respect to A(n) leads to a closed expression for the optimal dot density at every pass, or, in other words, to the optimal multi-pass system.