A new algorithm is proposed for constructing the implied recombining binomial tree. The implied tree built by the method is much more stable and reliable than that constructed using the algorithm of Derman and Kani (1994) and its extensions. Furthermore, it is faster and easier to use. The general properties of the implied model are studied. It is demonstrated that the local volatility function can become singular for certain volatility smiles. The implications of the singularity for the application of the implied model are discussed.