Because all existing accelerated initial stiffness schemes of the non linear FEM considering material's strain\|softening can not make sure of the convergence of iteration , based on the idea of secant stiffness method, a new accele rated initial stiffness scheme is put forward in this paper. It can be proved that the new method not only accelerates the iteration , but also assures the convergence of iteration even if the material's strain-softening is took into account.