The EM algorithm has become a popular efficient iterative procedure to compute the maximum likelihood (ML) estimate in the presence of incomplete data. Each iteration of the EM algorithm involves two steps called expectation step (E-step) and maximization step (M-step). Complexity of statistical model usually makes the iteration of maximization step difficult. An identity on which the derivation of the EM algorithm is based is presented. It is showed that deriving iteration formula of parameter of hidden binomial trials based on the identity is much simpler than that in common M-step.