Summary: In [the second author, SIAM J. Optim. 16, No.~4, 1110--1136 (2006; Zbl 1131.90029)], Roos proved that the devised full-step infeasible algorithm has \(O(n)\) worst-case iteration complexity. This complexity bound depends linearly on a parameter \(\bar{\kappa}(\zeta)\), which is proved to be less than \(\sqrt{2n}\). Based on extensive computational evidence (hundreds of thousands of randomly generated problems), Roos conjectured that \(\bar{\kappa}(\zeta)=1\) (Conjecture 5.1 in [loc. cit.]), which would yield an \(O(\sqrt{n})\) iteration full-Newton step infeasible interior-point algorithm. In this paper, we present an example showing that \(\bar{\kappa}(\zeta)\) is in the order of \(\sqrt{n}\), the same order as that proved in [loc. cit.]. In other words, the conjecture is false.