The earlier developed alternative technique for calculating the ionospheric contribution into the full phase of the signal on the transionospheric paths of propagation, based on the perturbation theory in spherical co-ordinates with the spherically symmetric inhomogeneous zero-order approximation for the ionosphere, is further extended in order to apply it to the two-frequency mode of operation of GNSS. When doing this, the method itself is additionally validated and verified in the numerical experiment, where the reconstruction of the slant TEC calculated by the alternative technique for the two-frequency mode of operation is compared to that directly generated by the NeQuick model of the ionosphere.