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This paper is devoted to studying the conversion of ordinary superluminous waves into extraordinary waves in an ultrarelativistic highly magnetized plasma of pulsars. The conversion appears to take place in the region of quasi-longitudinal propagation with respect to the magnetic field. Although the propagation of waves in pulsar magnetospheres is generally quasi-transverse, due to refraction the wave vector can for a short while become nearly aligned with the ambient magnetic field. As a result of the conversion, the originally ordinary wave turns into two waves, the ordinary and extraordinary. It is found that at pulsar conditions the conversion of the ordinary waves can be significant, i.e. a considerable part of the energy can be transmitted to the extraordinary waves. The process is suggested to underlie the observed transitions between the orthogonal polarization states in pulsar radiation. The connection of conversion with magnetospheric refraction implies a number of observational consequences which agree well with the observed features of the orthogonally polarized modes. In particular, it becomes possible to explain both the longitudinal location of the prominent orthogonal transitions and the high-frequency depolarization of pulsar radiation. Further polarization evolution of the natural waves resulting from the conversion is investigated as well. It is found that the polarization-limiting effect can account for both the change in the sense of circular polarization during the orthogonal transitions and the non-orthogonality of the observed modes. It is shown that any technique of mode separation should allow for the consequences of the polarization-limiting effect.