This paper presents a new bearing fault detection algorithm based on analyzing singular points of vibration signals using the Haar wavelet. The proposed Haar Fault Detection (HFD) algorithm is compared with a previously-developed algorithm associated with the Morlet wavelet. We also substitute the Haar wavelet with Daubechies wavelets with larger compact supports and evaluate the results. Simulations carried on real data demonstrate that the HFD algorithm achieves a comparable accuracy while having a lower computational cost. This makes the HFD algorithm an appropriate candidate for fast processing of bearing faults.