Speckle image reconstruction can effectively remove the influence of the atmospheric turbulence and obtain the diffraction limited images of the object. However, the static aberrations of the system can destroy the statistical information of the wavefronts and decrease the accuracy of the Fourier phase reconstruction. It shows that among defocus, astigmatism, coma and spherical aberration, only coma has residual phase on the reconstruction in ideal case. By dividing the pupil into several sub-apertures with Fried parameter as the diameter, the influence of the static aberration on the phases of the cross spectrum transfer function is analyzed. The result shows that by choosing the direction of the shift frequency in the cross spectrum transfer function, aberration balancing can be used to reduce the influence of the static aberration and improve the accuracy of the reconstruction. The simulations show desired effects of the balancing on the spherical aberration and defocus, astigmatism and defocus.