A new model for scintillation on transionospheric links, based on a hybrid method and valid for strong scintillations, has been developed and used to construct a software transionospheric channel simulator. The method is a combination of the complex phase method and the random screen technique. The parameters of the random screen are determined as the result of a rigorous solution to the problem of propagation inside the ionosphere using the extended Rytov approximation (the complex phase method). The random two-dimensional spatial spectrum at the screen is then transferred down to the Earth's surface employing the rigorous relationships of the random screen theory. Thus the complex phase method can adequately introduce a random screen below the ionosphere for L-band frequencies. The technique is capable of producing statistical characteristics and simulating time realizations of the field for a wide range of input parameters. Preliminary results are presented for both weak and strong scintillations.