We consider one-dimensional stochastic differential equations in the particular case of diffusion coefficient functions of the form|x|α , α ∈ [1/2,1). In that case, we study the rate of convergence of asymmetrized version of the Euler scheme. This symmetrized version iseasy to simulate on a computer. We prove its strong convergence and obtain the same rate ofconvergence as when the coefficients are Lipschitz.