This paper is concerned with the existence of Siegel disks of the Cremona map F α (x, y) = (x cos α − (y − x 2) sin α, x sin α + (y − x 2) cos α) with the parameter α ∈ [0, 2π). This problem is reduced to the existence of local invertible analytic solutions to a functional equation with small divisors λ n + λ −n − λ − λ −1. The main aim of this paper is to investigate whether this equation with |λ| = 1 has such a solution under the Brjuno condition.