It is recognized that the convergence of FFT based iterative schemes used for computing the effective properties of elastic composite materials drastically depends on the contrast between the phases. Particularly, the rate of convergence of the strain based iterative scheme strongly decreases when the composites contain very stiff inclusions and the method diverges in the case of rigid inclusions. Reversely, the stress based iterative scheme converges rapidly in the case of composites with very stiff or rigid inclusions, but leads to low convergence rates when soft inclusions are considered and to divergence for composites containing voids. It follows that the computation of effective properties is costly when the heterogeneous medium contains simultaneously soft and stiff phases. Particularly the problem of composites containing voids and rigid inclusions cannot be solved by the strain or the stress based approaches. In this paper, we propose a new polarization-based iterative scheme for computing the macroscopic properties of elastic composites with an arbitrary contrast which is nearly as simple as the basic schemes (strain and stress based) but which has the ability to compute the overall properties of multiphase composites with arbitrary elastic moduli, as illustrated through several examples.