In this paper, we propose a new two-parameterclass of iterative methods to solve a nonlinear equation. It is proved that any method in this class is .cubically convergent if and only if the parameters sum up to one. Some of existing third-order methods, by suitable selection of parameters, can be put in this class. Every iteration of the class requires on evaluation of the function, three of the first derivative, and none of the second derivative. Hence, its efficiency index is 3^{1/4} =1.316 thatis worse than all other cubically convergent methods considered. However, numerical experiments show that a special method fu our class is comparable to those in terms of iterations number.
