This paper proposes a method for generating a stable stealth walking gait without including the double-limb support phase on a frictionless road surface. First, we introduce a model of a planar underactuated rimless wheel with an upper body, and specify the target constraint condition of the total angular momentum around the ground contact point for maintaining the horizontal ground reaction force zero. Second, we derive an approximate analytical solution for the target initial state of the upper body by using the linearized equation of motion. Furthermore, we extend the results obtained to the nonlinear model, and numerically investigate the fundamental gait properties.