This paper is concerned with the state feedback stabilization problem of discrete-time singular systems. The singular system under consideration is not assumed to be regular. The problem we address is to design state feedback controllers such that the resulting closed-loop system is regular, causal and stable. Conditions for the existence of solutions to this problem are obtained, expressed in terms of certain matrix inequalities. When these conditions are satisfied, the explicit formula of desired state feedback controllers is also given without resorting to decomposing the system matrices.