A modified discretization ABS algorithm for solving a class of singular nonlinear systems, F($chi$)=0, where $chi$, F $in$ $R^n$, is presented, constructed by combining a discretization ABS algorithm arid a method of Hoy and Schwetlick (1990). The second order differential operation of F at a point is not required to be calculated directly in this algorithm. Q-quadratic convergence of this algorithm is given.