In this paper, we propose a new uniparametric family of modifications for Chebychev’s method, free from second derivatives, to solve non-linear equations. It is proved that each method in this family is cubically convergent. Every iteration of the family requires one evaluation of the function and two of the first derivative. Hence, the efficiency index of each method is 31/3 = 1,442 that is better than that of Newton’s method. Several numerical examples are, also, given to illustrate the performance of the presented method.
