Differential diagnosis of malignant melanoma, which is the cause of more than 75% of deaths amongst skin lesions, is vital for patients. Artificial intelligence-based decision support systems developed for the analysis of medical images are in the solution of such problems. In recent years, various deep learning algorithms have been developed to be used for this purpose. In our previous study, we compared the performances of AlexNet, GoogLeNet and ResNet-50 for the differential diagnosis of benign and malignant melanoma on International Skin Imaging Collaboration: Melanoma Project (ISIC) dataset. In this study, we proposed a CNN model by modifying the GoogLeNet algorithm and we compared the performance of this model with the previous results. For the experiments, we used 19,373 benign and 2197 malignant diagnosed dermoscopy images obtained from this public archive. We compared the performance results according to the eight different performance metrics including polygon area metric (PAM), classification accuracy (CA), sensitivity (SE), specificity (SP), area under curve (AUC), kappa (K), F measure metric (FM) and time complexity (TC) measures. According to the results, our proposed CNN achieved the best classification accuracy with 0.9309 and decreased the time complexity of GoogLeNet from 283 min 50 to 256 min 26 s.