The matrix inequality condition has been considered as the main condition for the stability of RHC. But it is difficult to apply the matrix inequality condition for guaranteeing the stability of any physical system because of the high gain problem brought about the high value of the final state weighting matrix. Therefore, in this study, a new stability condition for RHC is proposed and it extends the range of the final state weighting matrix guaranteeing the stability of RHC in comparison with the case of the matrix inequality condition. The proposed stability condition is based not only on a final state weighting matrix but also on a horizon size and guarantees the stability for other forms of model predictive control just like the matrix inequality condition.