In this paper, we prove that two multiplicative bias correction techniques (MBC) can be applied for discrete kernels in the context of probability mass function estimation. First, some properties of the MBC discrete kernel estimators (bias, variance and mean integrated squared error) are investigated. Second, the popular cross-validation technique is adapted for bandwidth selection. Finally, a simulation study and a real data application for discrete data illustrate the performance of the MBC estimators based on dirac discrete uniform and triangular discrete kernels.