In this paper, we study the rate of convergence of a symmetrized version of the classical Euler scheme, applied to the discretisation of the solution of a stochastic differential equation with a diffusion coefficient function of the form |x|^a, a in [1/2,1). For smooth test functions, we show that the weak error is of order one as for the classical Euler scheme. More over, the symmetrized version is very easy to simulate on a computer.