This letter investigates the asynchronous intermittent decentralized control for discrete-time large-scale systems with weak coupling. We assume that each subsystem admits independent and asynchronous intermittent activation/rest times. We design a discrete-time version auxiliary timer and construct vertex-Lyapunov function for each subsystem. We introduce an auxiliary digraph with time-varying weights and employ the tree-cycle identify to deal with the coupling between subsystems. We obtain linear matrix inequality (LMI) conditions for finding the maximal coupling strength and the minimal allowable averaging activation time of each intermittent controller that preserve the stability. An example of coupled inverted pendulums on two carts demonstrate the validity of our results.