Summary: We present a variant of Jarratt method with order of convergence six for solving non-linear equations [cf. J. Kou
and Y. Li
, Appl. Math. Comput. 189, No. 2, 1816–1821 (2007; Zbl 1122.65338
)]. Per iteration the method requires two evaluations of the function and two of its first derivatives. The new multistep iteration scheme, based on the new method, is developed and numerical tests verifying the theory are also given.