The authors discuss the application of a new k-stage collocation method for approximation to the two-point boundary value problem for an n- dimensional first order system of ordinary differential equations, and a single mth order equation, in case the system is stiff. New criteria for step size are presented in terms of the coefficients of the differential system. These criteria are applicable to stiff systems and insure that the system may be approximated by a one-step system of difference equations. The basis functions used in the collocation procedure form a so-called monomial basis [the second author, SIAM J. Numer. Anal. 23, 596-609 (1986; Zbl 0618.65072)]. The authors discuss implementation of the new algorithm by means of a new code called COLNEW which is a modification of the code COLSYS. The new code uses the monomial basis in place of a B-spline basis. Results with five difficult test examples are reported on. These indicate efficacy of the new code and improvement over the older code in accuracy and running time.