  In this article, we present an iterative method to find simple roots of
nonlinear equations, that is, to solving an equation of the form $f(x) = 0$.
Different from Newton's method, the method we purpose do not require evaluation
of derivatives. The method is based on the classical Steffensen's method and it
is a slight modification of it. The proofs of theoretical results are stated
using Landau's Little o notation and simples concepts of Real Analysis. We
prove that the method converges and its rate of convergence is quadratic. The
method present some advantages when compared with Newton's and Steffesen's
methods as ilustrated by numerical tests given.
