The uniform geometrical theory of diffraction is used to solve the 3D problem concerning the field from a circularly polarized radiator, diffracted by a perfectly conducting, infinitely thin plane rectangular screen. The radiator consists of two orthogonal pairs of mutually parallel half-wave dipoles, with excitation currents flowing through the dipole pairs being in quadrature. The patterns of the orthogonal field components are computed, including the power and polarization patterns within the entire observation space. It is shown that similar radiators, with appropriately chosen separations between the dipoles, may permit forming patterns of the orthogonal field components (as well as power patterns) possessing axial symmetry about the direction of the normal to the screen at observation angles ±45°...70°. The polarization pattern is close to an axially symmetric form at these angles, while being much wider than the polarization pattern of the classical circularly polarized turnstile dipole antenna with a screen.