For bandwidth selection in nonparametric regression, Haerdle, Hall, and Marron (1992) use the double smoothing technique to construct a bandwidth selector. However, this bandwidth selector uses extra smoothness of the regression function. In this paper, this bandwidth selector is modified to fit the usual regularity condition of the smoothness of the regression function. The limiting distribution of the bandwidth produced by the modified bandwidth selector is established. The effect of the number of continuous derivatives of the regression function on this modified bandwidth selector is precisely quantified through the limiting distribution. In the sense of the relative convergence rate of the bandwidth produced, the modified bandwidth selector is of better performance than both cross–validation and partitioned cross–validation.