  It is shown that the hydrodynamics equations for a thin spherical liquid
layer are satisfied by the stream function of a pair of antipodal vortices-APV,
in contrast to the stream function of a single point vortex on a sphere with a
background of a uniform opposite sign vorticity. A simple zero solution of the
equation of the absolute vorticity conservation is used for bypassing
well-known nonlinear problem of a point vortices interaction with regular
vorticity field and an exact solution for APVs dynamics problem on a rotating
sphere is obtained. Due to this a new stable stationary solution for the
dynamics of APV is obtained, which can model the dynamics of the global vortex
structures such as atmospheric centers of action.
