  For a random walk killed at leaving a cone we suggest two new constructions
of a positive harmonic function. These constructions allow one to remove a
quite strong extendability assumption, which has been imposed in our previous
paper (Denisov and Wachtel, 2015, Random walks in cones). As a consequence, all
the limit results from that paper remain true for cones which are either convex
or star-like and $C^2$.
