We study fairness in a multicast network. We assume that different receivers of the same session can receive information at different rates. We study fair allocation of utilities, where utility of a bandwidth is an arbitrary function of the bandwidth. The utility function is not strictly increasing, nor continuous in general. We discuss fairness issues in this general context. Fair allocation of utilities can be modeled as a nonlinear optimization problem. However, nonlinear optimization techniques do not terminate in a finite number of iterations in general. We present an algorithm for computing a fair utility allocation. Using specific fairness properties, we show that this algorithm attains global convergence and yields a fair allocation in polynomial number of iterations.