This paper is dedicated to a new binomial lattice method (MSM) consistent with the Black-Scholes model in the limit of an infinite step number and such that the Strike $K$ is equal to one of the final nodes of the tree. The method is very easy to implement, since the parameters are explicitly given. Asymptotic expansions are obtained for the MSM European Put price and delta, which motivates the use of Richardson extrapolation. A numerical comparison with the best lattice based numerical methods known in literature, shows the efficiency of the proposed algorithm for pricing and hedging American Put options.