An electrostatically charged Earth satellite whose orbit is decaying due to the Earth's oblateness is considered. Secular perturbations of the orbit are taken into account: they are caused by the second zonal harmonic of the geopotential. These perturbations represent deviations of the longitude of the ascending node and perigee argument, the orbit form being invariable and the orbit inclination to the equatorial plane being constant. The attitude rotary motion of the satellite under the action of perturbing moments of the gravitational and Lorentz forces is studied. The magnetic field of the Earth is taken in a quadrupole approximation. The evolution of the satellite's rotary motion is investigated on the basis of new differential equations in s-parameters specially constructed for this purpose. Using the method of averaging, basic regularities of the secular evolution of rotary motion of a screened satellite are revealed. It is found that the rotary motion of a charged satellite essentially depends on the quadrupole component of the geomagnetic potential.