Polycrystalline samples of shape memory iron-based alloys containing 17, and 30 mass% Mn and alloyed with Si, Cr, Ni, C, N were studied by means of small angle scattering of polarized neutrons (SAPNS). A direct correlation between chemical homogeneity of the Fe-Mn, Fe-Mn-Si, Fe-Mn-Si-Cr, Fe-Mn-Si-Cr-Ni solid solutions and the values of reversible strain caused by the γ → ε → γ martensitic transformation was found. The addition of silicon to the Fe-Mn alloys significantly improves chemical homogeneity of the fee solid solution on the scale of larger than several nm, which correlates with the essential increase of reversible strain. A similar to silicon but weaker effect was observed in the case of nitrogen addition to the Fe-Mn-Si-Cr, Fe-Mn-Si-Cr-Ni alloys. Based on the obtained experimental data and in consistency with the previously expressed idea by Sade et al., the positive effect of silicon and nitrogen on chemical homogeneity and SME in Fe-Mn alloys is attributed to the short-range atomic ordering induced by these elements.