This article presents the analysis of properties of functions belonging to the class Kn(D) earlier introduced by the author. This is a class of functions analytical in the domain D, for which the n-th divided difference [F; zo, . . . , zn] [...]consisting of functions univalent in the domain D is obtained. The subclass Kn(E), formed by functions F(z) = zn + an+izn+1 + .... analytical in a unit circle E is separated from class Kn(D) and its properties are considered. The author touches classical and at the same time urgent questions, arising at the study of analytical functions, belonging to some class.