A new method called C-C-1 method is suggested, which can improve some drawbacks of the original C-C method. Based on the theory of period , a new quantity for estimating the delay time window of a chaotic time series is given via direct computing a time-series quantity , from which the delay time window can be found. The optimal delay time window is taken as the first period of the chaotic time series with a local minimum of . Only the first local minimum of the average of a quantity is needed to ascertain the optimal delay time. The parameter of the C-C method - embedding dimension m - is adjusted rationally. In the new method, the estimates of the optimal delay time and the optimal delay time window are more appropriate. The robustness of the C-C-1 method reaches 40 %, whereas that of the C-C method is 30 %.