Let Xt(x) be the solution of stochastic differential equations with smooth and bounded derivatives coefficients. Let Xnt (x) be the Euler discretization scheme of SDEs with step 2−n. In this note, we prove that for any R > 0 and γ∈ (0, 1/2),
supt∈[0,1],|x|≤R|Xnt (x, ω) − Xt(x, ω)| ξ R, γ(ω)2−nγ, n > 1, q.e.,
where ξR, γ(ω) is quasi-everywhere finite.