[en] The short-distance contribution of the double penguin box diagram to the K⁰ - anti K⁰ mixing is investigated. Compared with previous work of other authors, the present paper takes into account the momentum dependence of the box loop, both the non-local part of the penguin and the previously considered local part and the crossed diagrams, which make a class of double penguin diagrams complete. With such new ingredients, is is concluded that the short-distance part of the double penguin is physically irrelevant. After eliminating this particular mechanism for the K⁰ - anti K⁰ mixing, other potentially relevant mechanisms are pointed out