The objective is to investigate the singular problem of the robot control scheme with (usinθ) as the orientation error presented elsewhere, where u and θ are, respectively, the unit vector of the rotational axis and the rotational angle from the current orientation of the end-effector to the desired one. The singularity analysis of the control scheme is important to its practical applications. It is rigorously found that the singular points of the control scheme are θ = ± π/2 and ± π, and for a step input θ, π/2 < |θ| < π, the orientation error converges to θ = π instead of θ = 0. Therefore, the applicable domain of this control scheme is only — π/2 < θ < π/2. The theory is also verified by the simulations that were run on the Stanford manipulator.