Abstract—In this paper, the estimation of a nonlinear stochastic dependence between signals in information-measuring and control systems is considered. The maximum correlation coefficient and corresponding optimal transformations of the signals are estimated using the Bernstein approximation. Some basic concepts of the copula theory are discussed. Main calculation formulas for the maximum correlation coefficient in the case of a degenerate stochastic kernel are presented. An estimation algorithm for the maximum correlation coefficient and corresponding optimal (nonlinear) transformations of random signals is proposed. An example of correlation estimation for random signals is given.