This paper proposes a new method to solve the post-nonlinear blind source separation problem (PNLBSS). The method is based on the fact that the distribution of the output signals of the linearly mixed system are approximately Gaussian distributed. According to the central limit theory, if one can manage the probability density function (PDF) of the nonlinear mixed signals to be Gaussian distribution, then this means that the signals becomes linearly mixed in spite of the PDF of its separate components. In this paper, the short time Gaussianization utilizing the B-spline neural network is used to ensure that the distribution of the signal is converted to the Gaussian distribution. These networks are built using neurons with flexible B-spline activation functions. The fourth order moment is used as a measurement of Gaussianization. After finishing the Gaussianization step, linear blind source separation method is used to recover the original signals. Performed computer simulations have shown the effectiveness of the idea, even in presence of strong nonlinearities and synthetic mixture of real world data.