The improved quadrilateral discretization model for the topology optimization of compliant mechanisms is introduced in this paper. The design domain is discretized into quadrilateral design cells and each quadrilateral design cell is further subdivided into triangular analysis cells. All kinds of dangling quadrilateral design cells and sharp-corner triangular analysis cells are removed in the improved quadrilateral discretization model to promote the material utilization. Every quadrilateral design cell or triangular analysis cell is either solid or void to implement the discrete topology optimization and eradicate the topology uncertainty caused by intermediate material states. The local stress constraint is directly imposed on each triangular analysis cell to make the synthesized compliant mechanism safe. The binary bit-array genetic algorithm is used to search for the optimal topology to circumvent the geometrical bias against the vertical design cells. Two topology optimization examples of compliant mechanisms are solved based on the proposed improved quadrilateral discretization model to verify its effectiveness.