Cardiac auscultation is one of the most conventional approaches for the initial assessment of heart disease, however the technique is highly user-dependent and with low repeatability. Several computational approaches based on the analysis of the phonocardiograms (PCG) have been proposed to classify heart sounds into normal or abnormal, but most often do not achieve acceptable levels of sensitivity (Se) and specificity (Sp) or require the use of special hardware. We propose a novel approach for classification of PCG. First, the system makes use of deep neural networks for computing individual cardiac cycle probabilities, followed by classification using weighted probability comparisons. The system was tested on an extended dataset consisting of a balanced sample of 18179 normal and abnormal cycles, achieving Se and Sp values of 91.3% and 93.8% respectively. In addition, the system overcomes previous limitations since it was trained with a balanced sample; also, the decision factor used during the classification stage allows to control the trade-off between Se and Sp, making the proposed system suitable for clinical applications.