In this paper a novel method for gait trajectory design of a point legged quadruped robot with 18 degree of freedom on a flat surface is proposed. The exact model of the mechanical parts of the robot including four legs and the body and all joints will be derived and used in gait trajectory planning. Inverse dynamics of the quadruped are formulized using Denavit-Hartenberg (DH) convention. Bezier curves are used for trajectory planning. Effects of body and legs on Zero Moment Point (ZMP) will be analyzed separately. By manipulating free parameters, a stable gait trajectory will be designed according to ZMP dynamic stability criterion. Simulations are done using Matlab and Mathematica software which show good performance of the novel method proposed.