  An exact closed equation for s - particle equilibrium distribution function
(s<N) of the system of N>>1 interacting particles is obtained. This
integra-differential {\beta} - convolution equation ({\beta}=1/k_{B}T) follows
from the Bloch equation for the canonical distribution function by applying the
projection operator integrating off the coordinates of N-s irrelevant
particles. The method of expansion of the obtained equation kernel in the
particle density n is suggested. The solution to this equation in the linear in
n approximation for the kernel is found.
