The multiple phase screen method is widely used for modelling the electromagnetic propagation in a turbulent medium. In this technique, the turbulent phase screens are classically generated from a continuous Von-Karman Kolmogorov scintillation spectrum. Recent works led to the development of an auto-coherent split-step wavelet propagation method based on a discrete formulation of the parabolic wave equation. In this configuration, the use of continuous spectra is no more suitable. In this paper, we propose an auto-coherent generation method of the turbulent phase screens. To do so, a discrete formulation of the classical Von-Karman Kolmogorov spectrum is introduced. The impact of the modelled turbulence is finally discussed through the computation of the log-amplitude variance to validate this approach.