  The system of second-order equations of mean-field expansion is considered
for Nambu--Jona-Lasinio model with chiral symmetry of SU(2)-group. The system
includes equations for four-particle and three-particle functions and also
equations for next-to-leading two-particle function and next-to-next-to-leading
quark propagator. Exact solutions for four-particle and three-particle
equations are obtained. The solution for four-particle function is a
disconnected combination of the leading-order two-particle functions. The
connected part of three-particle function includes two-meson and three-meson
contributions. The solution of three-particle equation permits to close the
equation for next-to-leading two-particle function and to calculate a
correction to pion-decay constant $f_\pi$. This correction increases from 14%
to 28% when values of quark condensate varies from $-(210 MeV)^3$ to $-(250
MeV)^3$.
