In this paper, we present two new one-step iterative methods based on Thiele-s continued fraction for solving nonlinear equations. By applying the truncated Thiele-s continued fraction twice, the iterative methods are obtained respectively. Analysis of convergence shows that the new methods are fourth-order convergent. Numerical tests verifying the theory are given and based on the methods, two new one-step iterations are developed., {"references":["R.L. Burden, J.D. Faires, Numerical Analysis (Sixth ed.), Brooks/Cole\nPublishing Company, Calif., 1997.","J. Stoer, R. Bulirsch, Introduction to Numerical Analysis (Third ed.),\nSpringer-Verlag, New York, 2002.","A. Quarteroni, R. Sacco, F. Saleri, Numerical Mathematics, Springer-\nVerlag, New York, 2000.","J.Q. Tan, The limiting case of Thiele-s interpolating continued fraction\nexpansion, J. Comput. Math. 19 (2001), pp. 433-444.","J.Q. Tan, The Theory of Continued Fraction and Its Applications,\nScience Publishers, Beijing, 2007.","S. Weerakoon, T.G.I. Fernando, A variant of Newton-s method with\naccelerated third-order convergence, Appl. Math. Lett. 13 (2000), pp.\n87-93.","J. Kou, Y. Li, A family of modified super-Halley methods with fourthorder\nconvergence, Appl. Math. Comput. 189 (2007), pp. 366-370.","J. Kou, Some variants of Cauchy-s method with accelerated fourth-order\nconvergence, J. Comput. Appl. Math. 213 (2008), pp. 71-78.","C. Chun, Y. Ham, Some fourth-order modifications of Newton-s method,\nAppl. Math. Comput.197 (2008), pp. 654-658.\n[10] I.K. Argyros, A note on the Halley method in Banach spaces, Appl.\nMath. Comput. 58 (1993), pp. 215-224.\n[11] J.M. Guti'errez, M.A. Hern'andez, An acceleration of Newtons method:\nsuper-Halley method, Appl. Math. Comput. 117 (2001), pp. 223-239.\n[12] J.M. Guti'errez, M.A. Hern'andez, A family of Chebyshev-Halley type\nmethods in Banach spaces, Bull. Austral. Math. Soc. 55 (1997), pp.\n113-130.\n[13] J. Kou, Y. Li, X. Wang, Fourth-order iterative methods free from second\nderivative, Appl. Math. Comput. 184 (2007), pp. 880-885.\n[14] S. Abbasbandy, Improving Newton-Raphson method for nonlinear equations\nby modified Adomian decomposition method, Appl. Math. Comput.\n145 (2003), pp. 887-893.\n[15] J. Kou, Y. Li, X. Wang, A composite fourth-order iterative method for\nsolving non-linear equations, Appl. Math. Comput. 184 (2007), pp. 471-\n475.\n[16] J. Kou, X. Wang, Y. Li, Some eighth-order root-finding three-step\nmethods, Commun. Nonlinear Sci. Numer. Simulat. 15 (2010), pp. 536-\n544.\n[17] X. Wang, J. Kou, C. Gu, A new modified secant-like method for solving\nnonlinear equations, Computers and Math. with Appl. 60 (2010), pp.\n1633-1638."]}