Summary: D. W. Clarke proposed a Generalized Predictive Control (GPC) algorithm in \textit{D. W. Clarke}, \textit{C. Mohtadi} and \textit{P. S. Tuffs} [Automatica 23, 149-160 (1987; Zbl 0621.93033) and ibid. 23, 137-148 (1987; Zbl 0621.93032)]. We have proposed a modified control algorithm. In this paper, the stability this modified control algorithm is analyzed. The characteristic polynomial of the loop system is simply expressed, its parameters are directly obtained from predictive model parameters requiring no further computation. Its conclusions are still suitable to the analysis of the original GPC algorithm.