Abstract: In this paper a class of the extended second derivative formulas is presented. Based on the extended k-step second derivative formula a new predictor-corrector method called Extended k-step second Derivative Method for stiff systems is formulated with the k-step second derivative formula as its implicit predictor. The extended second derivative methods have the higher orders and the better stability properties. The computational effort is comparitively large, but much of it can be saved, so that the methods are acceptable and efficient.