For functions*f(x)* representable by an integral operator of a special form, we investigate the behavior of the second difference Δ
_{h}^{2}*f*(*x*)=*f*(*x*+*h*)-2*f*(*x*)+*f*(*x*-*h*),*h*>0, depending on the location of a point*x* on the segment [0,1].