The kinematical properties of the Galactic thick disk are studied using absolute proper motions from the Third Yale/San Juan Southern Proper Motion Catalog and Two Micron All Sky Survey near-infrared photometry for a sample of ~1200 red giants in the direction of the south Galactic pole. The photometrically selected sample is dominated by thick-disk stars, as indicated by the number-density distribution that varies with distance from the Galactic plane as a single-valued exponential over the range 1 kpc < z < 4 kpc. The inferred scale height of the thick disk is 0.783 ± 0.048 kpc. The kinematics of the sample are also consistent with disklike motion. The U-velocity component is roughly constant, reflecting the Sun's peculiar motion, while a considerable shear is seen in the mean rotational velocity, V. The V-velocity profile's dependence on z is linear, with a gradient of dV/dz = -30 ± 3 km s-1 kpc-1. The velocity dispersions in both U and V show a lesser gradient of about 9 ± 3 km s-1 kpc-1. We demonstrate that the derived velocity and velocity-dispersion profiles are consistent with the assumptions of dynamical equilibrium and reasonable models of the overall Galactic potential.