The supplementary variable technique(SVT) is a popular method for analyzing various queueing models. The results obtained by the SVT are expressed in terms of transforms. Recently, a modified SVT is introduced and used for analyzing continuous-time queues. The results obtained by the modified SVT are transform-free. The purpose of this paper is to demonstrate that the modified SVT can be used for analyzing discrete-time queues as well. We consider the discrete-time GI/G/1/K queue under the assumption of the early arrival system. As a result, we present the steady-state distribution of the queue length in terms of conditional expectations of the remaining interarrival time and the remaining service time, conditional on the queue lengths at the departure points and the arrival points, respectively.