A calculation of the local magnetization in thes-d model is made up to terms of second order in «J ». It is shown that, assuming a constant density of states symmetric about the Fermi level, one obtains a singular contribution to the local magnetization in the limit of small magnetic fields whose value is\(\left\langle {S^z } \right\rangle _{\sin g} \sim J^2 \left\langle {(S^2 )^2 } \right\rangle _{H = 0} [4\beta \Delta \omega _0 \ln \beta D + 2\beta \omega _0 \ln \beta D]\), whereD is the half-width of the density of states and Δω0 is proportional to the difference in «g » factors. The evaluation of all integrals leading to the above result is discussed in detail.