The main purpose of this paper is to investigate the detection of jump points of a discontinuous function in the presence of a noise by the wavelet approach. A computing algorithm of our method is proposed and then applied to the daily exchange rate of US Dollar against Deutsche Mark. All the points detected by our method reflect very strong economic and political impacts. Other statistical methods to detect jump points have also been applied to the same exchange rate data. Our proposed method has produced more convincing empirical results than others.