The authors propose a two-step iterative method for the solution of the nonlinear equation \(f(x)=0\) with sufficiently smooth \(f\) and show that this method has convergence order six. In the proposed method, each step merely consists of one step with the classical second-order Newton method and a subsequent step with the classical third-order Halley method. It is not surprising that these two steps combined lead to a sixth-order convergence.