Functional iteration has been very widely used for the solution of nonlinear system equations. Although sufficient conditions have been given for the iteration sequence to converge, a method to determine the precise number of iterations that are required is not to be found in the literature. The availability of such information would enhance, considerably, the utility of the method. Using the concept of ‘stop-growing terms’, an algorithm is now proposed which enables one to determine precisely the number of iterations that are required for the solution to converge to a predetermined degree of approximation.