Let a function f be holomorphic in the unit ball ⁿ, continuous in the closed ball B¯ ⁿ , and let f(z) ≠ 0, z ∈ ⁿ. Assume that |f| belongs to the α-Hölder class on the unit sphere S ⁿ, 0 < α ≤ 1. The present paper is devoted to the proof of the statement that f belongs to the α/2-Hölder class on B¯ ⁿ.