This paper formulates a new scheme for time-optimal nonlinear model predictive control (TONMPC). In contrast to other TONMPC schemes for point-to-point motions found in the literature, it does not require a time transformation or a time scaling, which facilitates a stability proof. The practical applicability is shown with hardware-in-the-loop (HIL) experiments on an embedded platform using an illustrative control example, along with a comparison to one other time-optimal controller.