Concerning the existence of Krein graphs Kre(\(r\)), a lemma in [S. R. Zaripov, A. A. Makhnev and I. P. Yablonko, On strongly regular triangle-free graphs. In: Algebra and linear optimization. Proc. of the international seminar, dedicated to S. N. Chernikov on the occasion of his 90th birthday, Ekaterinburg, 117-121 (2002; Zbl 1009.20001)] involved an arithmetical error. In the present paper this error is corrected. The authors show that any Krein graph Kre(\(r\)) does not contain any subgraph \(K_{r,r}\) for \(r\geq 9\) and, by using a graph-theoretical argument, the nonexistence of Kre(3) (i.e., strongly regular graphs with parameters \((324,57,0,12)\)) is proved.