The binomial transformer is a well known concept in impedance matching. By the use of multiple quarter wavelength sections broadband matching is achieved. Many textbooks handle the problem starting from the approximated theory of small reflections. In this paper, a new and exact derivation for the impedances of the different sections is given. It is shown that not the section coefficients must satisfy a binomial distribution (as commonly used), but a transformation of these coefficients. Furthermore, an alternative formulation starting form the theory of small reflections is given. The results of the different methods are compared. It is shown that the alternative formulation gives the best agreement with the exact method.