We define a crossing point $x_0$ such that f(x)$geq$g(x) for x$leq$$x_0$ and f(x)$leq$g(x) for x>$x_0$ where f and g are probability density functions. We may encounter suchy situation when we compare two histograms from two independent observations. For example two contingency tables where initially admitted students and actually enrolled students are classified according to their high school ranking may show such situation, In this paper we consider maximum likelihood estimation of cell probabilities when a crossing point exists, We first assume a known crossing point and find an estimator. The estimation procedure for the case of unknown crossing point is just a straightforward extension. A real data is analyzed for an illustrative purpose.