In this paper we present an implicit two-point block method for solving directly the general second order ordinary differential equations (ODEs).The method incorporates the first and second derivatives of f(x, y, y ), which are the third and fourth derivatives of the solution.The method is derived using Hermite Interpolating Polynomial as the basic function.A performance comparison of the two-point block method is compared in term of accuracy to several existing methods, which have order almost equal or higher tha…