From the text: This catenoid is a complete discrete minimal surface given by explicit formulas for its vertices. The authors have found an explicit representation of a 4-parameter family of complete discrete catenoids. These catenoids are the first explicitly known discrete versions of a complete minimal surface beside the trivial plane which are solutions of the variational problem for the discrete surface area. This explicit representation allows to generate exact discrete minimal surfaces without numerical errors which is useful, for example, in index computations.