We expand the celebrated Alòs decomposition formula of the call price under the Heston model in a Taylor type series of in nite stochastic terms. This expansion is a di erent representation of a formula given in a recent paper by Alòs, Gatheral and Radoi£i¢. We use our expansion to obtain di erent approximations of the call price with precise estimations of the error order. These approximations improve the approximations available in the literature. With ve terms we obtain a theoretical error of O(ν 3 (|ρ| + ν)) where ν is the vol-vol and ρ is the correlation between the price and the volatility. With seven terms more we obtain a theoretical error of O(ν 4 (1 + |ρ|) that improves the approximation in the correlated case. In particular, for the zero correlation case, we have an approximation of order O(ν 6 ) with only four terms. Numerical experiments show that these approximating formulas perform especially well for high volatility mode.