In this study, stability conditions of receding horizon control (RHC) based on a horizon size are proposed for linear discrete systems. The proposed stability conditions present a relevant horizon size which can guarantee the stability of RHC even though a final state weighting matrix does not satisfy non-increasing monotonicity of optimal cost. Therefore, the possible range of the final state weighting matrix ensuring the stability of RHC is extended to zero and also it can be applied to the stability problems of other forms of model predictive control like the conventional stability conditions.