This note addresses global asymptotic stabilization of a class of discrete-time descriptor bilinear systems via a saturated state feedback controller. Based on LaSalle invariance principle and the implicit function theorem, sufficient conditions are presented to guarantee the uniqueness and existence of solution and the global asymptotic stability of the resulting closed-loop systems simultaneously. It is shown that the condition is independent of the state transformation for the given descriptor systems. Furthermore, the effectiveness of the proposed design method is illustrated by a numerical example.