This work deals with the problem of electromagnetic field propagation in the turbulent ionosphere with intermittency effects taken into account. The intermittency is involved through introducing the multifractal stochastic distribution of irregularities that implies the non-Gaussian statistics of the electron density fluctuations. The propagation problem is simulated utilizing the random screen technique. The algorithm of generation of the spatial distribution of the stochastic phase on the screen employs the two-dimensional inverse discrete wavelet transform. The wavelet coefficients are generated utilizing the stochastic lognormal cascade on the dyadic tree. The statistical characteristics of the field fluctuations after passing the phase screen are studied, and the peculiarities of the field statistics due to the non-Gaussianity of the screen are demonstrated and discussed.