Mechanical wear and defective bearings can cause machinery to reduce its reliability, safety and efficiency. Therefore it is very important to take care of bearings during maintenance and detect their faults in an early stage in order to assure safe and efficient operation. We present a new technique for an early fault detection and diagnosis in rolling-element bearings based on vibration signal analysis. After normalization and the wavelet transform of vibration signals, the logarithmic energy entropy as a measure of the degree of order/disorder is extracted in a few sub-bands of interest. Then the feature space dimension is optimally reduced to two using scatter matrices. In the reduced two-dimensional feature space the fault detection is performed by a quadratic classifier and the fault diagnosis by another two quadratic classifiers. Accuracy of the new technique was tested on the ball bearing data recorded at the Case Western Reserve University Bearing Data Center. In total four classes of the vibrations signals were studied, i.e. normal, with the fault of inner race, outer race and balls operation. An overall accuracy of 100% was achieved. The new technique can be used to increase productivity and energy efficiency by preventing unexpected faulty operation of machinery bearings.