This paper investigates the extent of nonstationarity of beta across the firm size and the beta magnitude by suggesting the sequential parameter stationarity model and estimating change-points of betas. The high-beta firm has shorter stationary interval, which means that its beta changes more frequently than do the low-beta firm's. The firm size, however, does not have a monotonic relation with the length of stationary interval. The small and large firms have relatively shorter stationary interval than do the mid-sized firms. The average length of stationary interval is estimated about five years (exactly 54.19 months). This fact could support the currently widely-used arbitrary 5-year assumption of beta stationarity. The fluctuation of the large firm's beta is more severe than the small firm's, and the high- and low-beta firms have the relatively greater fluctuating betas than do the mid-beta firms. The frequency of detected change-points is found to be positively related to market returns. When the market return is high, the systematic risk changes more frequently, and vice versa.