Some of the factors affecting the accuracy of positioning with the OMEGA radionavigation system are discussed. A simplified algorithm of computing the diurnal corrections for OMEGA is developed. It is based on the calculation of the mean velocity of propagation of VLF radiowaves as a function of the effective height of a spherical waveguide. The formulae to compute the latter are given. A composite signal method proposed by Pierce and its modification by Papousek and Reder are discussed; it is shown that the accuracy of the modified version is not better than that of the original. Both in Pierce's method and its modifications the waveguide is treated as a plane. Its sphericity is taken into account in this article, which results in better compensation of the phase variations of OMEGA signals. It is shown that fractionally rational transformations of the phase count may result in an additional error. To reduce that error, a high reliability of the ambiguity resolution is required at all used frequencies.