Heart murmurs often indicate heart valvular disorders. However, not all heart murmurs are organic. For example, musical murmurs detected in children are mostly innocent. Because of the challenges of mastering auscultation skills and reducing healthcare expenses, this study aims to discover new features for distinguishing innocent murmurs from organic murmurs, with the ultimate objective of designing an intelligent diagnostic system that could be used at home. Phonocardiographic signals that were recorded in an auscultation training CD were used for analysis. Instead of the discrete wavelet transform that has been used often in previous work, a continuous wavelet transform was applied on the heart sound data. The matrix that was derived from the continuous wavelet transform was then processed via singular value decomposition and QR decomposition, for feature extraction. Shannon entropy and the Gini index were adopted to generate features. To reduce the number of features that were extracted, the feature selection algorithm of sequential forward floating selection (SFFS) was utilized to select the most significant features, with the selection criterion being the maximization of the average accuracy from a 10-fold cross-validation of a classification algorithm called classification and regression trees (CART). An average sensitivity of 94%, a specificity of 83%, and a classification accuracy of 90% were achieved. These favorable results substantiate the effectiveness of the feature extraction methods based on the proposed matrix decomposition method.