This technical note is concerned with stability of linear discrete-time systems with interval-like time-varying delays. Two new stability criteria are derived by constructing a new Lyapunov functional and utilizing two novel techniques for estimating the forward difference of the Lyapunov functional. The relationship between these stability criteria and some existing ones is established. Through the relationship, it is clear that these stability criteria are less conservative than some existing ones, which is confirmed by a numerical example.