The motion of a nonsymmetric satellite about its center of mass in the neighborhood of a relative equilibrium in a circular orbit is investigated. The Norma specialized software package [1] intended for normalization of autonomous Hamiltonian systems is used to construct the normal form of the Hamiltonian and the normalizing transformation of the canonical variables. This provides an analytical solution of the problem in the neighborhood of the equilibrium. Normalization up to the 4th order of the Hamiltonian expansion in the coordinates and impulses is accomplished. To spare computer main memory, a procedure of redefinition of coefficients of the generating function and auxiliary polynomials is used at various stages of normalization. The dependence of the error of analytical solutions on time is studied for long time intervals. It is shown that the observed error is caused mainly by a difference between the actual values of the system frequencies and their approximations in the normalized system. This is why the error increases, on the average, linearly with time as a consequence of an increase of the time displacement between the exact and analytical solutions.