The auscultation of heart sounds has been for decades a fundamental diagnostic tool in clinical practice. Higher effectiveness can be achieved by recording the corresponding biomedical signal, namely the phonocardiographic signal, and processing it by means of traditional signal processing techniques. An unavoidable processing step is the heart sound segmentation, which is still a challenging task from a technical viewpoint—a limitation of state-of-the-art approaches is the unavailability of trustworthy techniques for the detection of heart sound components. The aim of this work is to design a reliable algorithm for the identification and the classification of heart sounds’ main components. The proposed methodology was tested on a sample population of 24 healthy subjects over 10-min-long simultaneous electrocardiographic and phonocardiographic recordings and it was found capable of correctly detecting and classifying an average of 99.2% of the heart sounds along with their components. Moreover, the delay of each component with respect to the corresponding R-wave peak and the delay among the components of the same heart sound were computed: the resulting experimental values are coherent with what is expected from the literature and what was obtained by other studies.