Independent Component Analysis (ICA) aims to find a coordinate system in which the components of the data are independent. In this paper we construct a new nonlinear ICA model, called WICA, which obtains better and more stable results than other algorithms. A crucial tool is given by a new efficient method of verifying nonlinear dependence with the use of computation of correlation coefficients for normally weighted data. In addition, authors propose a new baseline nonlinear mixing to perform comparable experiments, and a~reliable measure which allows fair comparison of nonlinear models. Our code for WICA is available on Github https://github.com/gmum/wica.