  The retarded Green's function G(k,\omega) of a single small spin polaron in
the three-band model for the CuO_2 plane is calculated in the self-consistent
Born approximation. It is shown that such a spin polaron is a good
quasiparticle excitation for realistic values of spin exchange J and effective
hopping \tau. The polaron spectral density A_p(k,\omega) demonstrates small
damping in contrast to the results of calculations starting from the bare hole,
i.e. the pole strength of the energetically low-lying quasiparticle peak Z_p(k)
varies from 50% to 82% for J/\tau ~ 0.1/0.7. The quasiparticle peak dispersion
reproduces the main features of the bare polaron spectrum \Omega_k near the
band bottom. The spherically symmetric approach is used for the description of
spin excitations. It makes it possible to consider the quantum
antiferromagnetic background without the spontaneous symmetry breaking and the
unit cell doubling. The new method of the self-consistent calculation, based on
continued fraction expansion of Green's function, is represented in details.
The method preserves the proper analytical properties of the Green's function
and provides the possibility to analyze the nature of its singularities.
