This paper presents a novel method for discrimination between innocent and pathological murmurs using the growing time support vector machine (GTSVM). The proposed method is tailored for characterizing innocent murmurs (IM) by putting more emphasis on the early parts of the signal as IMs are often heard in early systolic phase. Individuals with mild to severe aortic stenosis (AS) and IM are the two groups subjected to analysis, taking the normal individuals with no murmur (NM) as the control group. The AS is selected due to the similarity of its murmur to IM, particularly in mild cases. To investigate the effect of the growing time windows, the performance of the GTSVM is compared to that of a conventional support vector machine (SVM), using repeated random sub-sampling method. The mean value of the classification rate/sensitivity is found to be 88%/86% for the GTSVM and 84%/83% for the SVM. The statistical evaluations show that the GTSVM significantly improves performance of the classification as compared to the SVM.