On-line solution of system of nonlinear equations is required in several areas of chemical engineering. Failure of currently available numerical methods to converge to a solution or convergence to an infeasible solution creates problems. For these applications, methods are needed that would find a feasible solution within specified bounds without breaking down. Since bracketing methods offer a high probability of convergence, an extension of the well-known bracketing method is presented in this paper. Its performance is demonstrated on 12 example problems from the chemical engineering literature. The high probability of convergence obtainable makes the proposed method a viable candidate for consideration.