On a conjecture of Gohberg and Rodman (Q750567)

\textit{I. Gohberg} and \textit{L. Rodman} [Linear Algebra Appl. 76, 85-120 (1986; Zbl 0586.15001)] have given an algorithm to construct a sequence of matrices supposedly satisfying certain conditions related to Conjecture 7.2 in that paper. The author of the present paper shows that this construction fails to satisfy those conditions. The author gives a different sequence having the desired properties along with verifying the conjecture for another special case. The author also shows that the conjecture, in its generality, is false. The author gives examples of cases when the conjecture is false and when the conjecture is true.