Biorthogonal spline wavelet is used to detect the QRS complex of ECG signal. Mallat algorithm is applied in the decomposition of ECG signal by using the equivalent filter of a biorthogonal spline wavelet. Lipschitz exponent is introduced to investigate the relationship between the signal singularity (R Peak) and the zero-crossing point of the modulus maximum pair of the signal's wavelet transform. Adaptive threshold, refractory period and expiating are applied to improve the anti-interference performance. Experimental results demonstrated that this method is robust against time varying characteristics of QRS complex and noise. A correct detection rate of 99.905% has been achieved when the MIT-BIH Arrhythmia Database is used to test the proposed QRS complex detection algorithm.