Employing the standard observer architecture to embed a neural network to estimate the states as well as uncertainty of a dynamic system, the modified state observer(MSO) is a technique that has found some successful applications in the engineering community, such as orbit uncertainty estimation problem, atmospheric reentry uncertainty estimation problem, and control design problem of nonlinear electrohydraulic system with parameter uncertainty. For implementation, however, it is desirable to have a discrete version that can be built into a microcontroller. In this paper, we formulate the discrete time version of the MSO, called the discrete time modified state observer (DMSO). Necessary mechanisms are developed using the Lyapunov theory. Finally, to prove the validity of the discrete time modified state observer, simulation studies are performed using a two wheeled inverted pendulum robot, a benchmark unstable nonlinear system.