We consider experimentally the evolution of polarization singularities in singular beams transmitting at some angle to the optical axis of the LiNb03 crystals. We focused our attention on the processes of birth and annihilation of coupled singularities and compared them with those in a computer-simulation experiment. The conditions of the unfolding of the polarization singularities were brought to light. A number of difficulties arising in the course of the experiment are discussed.