This paper proposes a new model of an underactuated rimless wheel (URW) that added a reaction wheel for easily generating a non-slippery stealth walking gait. First, we introduce a 3-DOF URW model that can utilize two control torques, and describe the equation of motion. Second, we develop a controller for achieving strict output-following control of the stance-leg angle and angular momentum constraint control simultaneously. Third, we derive an approximate analytical solution of the target initial states of the upper body and reaction wheel. Furthermore, we propose a simple numerical procedure for identifying the target initial state of the nonlinear model, and investigate the effectiveness through numerical simulations.