We give an other proof of the classical Beurling theorem on z-invariant subspaces in the classical Hardy space H-2(D) over the open unit disk D, in which the concept of Berezin symbol is not used (see M.T. Karaev [On some problems related to Berezin symbols, C. R. Acad. Sci. Paris, Ser. 1340 (10) (2005) 715-7181). This improves the author's proof in Karaev (2005). (C) 2006 Elsevier GmbH. All rights reserved.