Abstract: A new iterative algorithm is presented for seeking the design point in the FOSM reliability index analysis. Based on a deeper insight into the poor convergence of available iteration schemes, a criterion is suggested to detect zigzagging movements of the solutions. A modification to the design point predicted by the classical HL-RF method is proposed to eliminate excessive zigzagging iterations. The proposed method is based on the interpolation techniques. Numerical examples show that the present method is capable of alleviating zigzagging movements in the iteration history, and more effective in convergence and stability of iterations than the classical HL-RF method and the other methods in the related references.