ABSTRACT Single-pulse data on radio pulsar polarization are traditionally presented in the form of two-dimensional grey-scale patterns with the pulse longitude and polarization angle (PA) on the horizontal and vertical axis, respectively. Such diagrams reveal several enigmatic polarization effects: (1) bifurcations and loops of PA curve under central pulse components, (2) vertical spread of flux at all PA values, (3) exchange of power content between PA tracks of two orthogonal polarization modes (OPMs), and (4) peripherically flat PA swings that span more than 180 deg. It is shown that all these phenomena result from passage of observed polarization state near the pure-V pole of Poincaré sphere. Much of their complexity results from cartographic transformation from Poincaré sphere to the longitude–PA plane. An odd number of near-pole passages produce apparent replacement of OPM power in the profile wings, although the same amount of flux keeps staying in each modal patch on the Poincaré sphere. The fitting of pulsar PA curves should therefore allow for transitions between the primary (strong) and secondary (weak) PA tracks. The Stokes space (or Poincaré sphere) representation of pulsar polarization data contains crucial polarization information and needs to accompany the traditional viewing if the published figures are to be fully useful for interpretation.