The paper is devoted to the stability analysis of the explicit two-step methods for the Cauchy problem solution, based on the extended Runge - Kutta-like formula. A feature of the methods is the use of the derivative of the differential equation’s right part, which is approximated by finite differences. The dependence of the coefficients of the stability polynomials on the free parameter is demonstrated. It provides the possibility to improve the stability by choosing the parameter values, since the geometric characteristics of the stability domain are dependent on the parameter. The role of the parameter values in the method stabilization is demonstrated by the solution of the problem for stiff Van Der Pohl equation.