In this paper, using an equivalent characterization of the Besov space by its wavelet coefcients and the discretization technique due to Maiorov, we determine the asymptotic degree of the Bernstein n-widths of the compact embeddings Bs+t q0(Lp0(Ω)) → Bs q1(Lp1(Ω)), t > max{d(1/p0 1/p1), 0}, 1 ≤ p0, p1, q0, q1≤∞, where Bs+t q0(Lp0(Ω)) is a Besov space defned on the bounded Lipschitz domain Ω Rd. The results we obtained here are just dual to the known results of Kolmogorov widths on the related classes of functions.