We prove that if a function f is holomorphic in the polydisk 픻 ⁿ, n ≥ 2, f is continuous in D ⁿ¯ , f(z) ≠ 0, z ∈ 픻 ⁿ, and |f| belongs to the α-Hölder class, 0 < α < 1, on the boundary of 픻 ⁿ, then f belongs to the (α2−ε)-Hölder class on D ⁿ¯ for any ε > 0.