This article refers to the Computer Aided Diagnosis of the melanoma skin cancer. We derive wavelet-based features of melanoma from the dermoscopic images of pigmental skin lesions and apply binary C-SVM classifiers to discriminate malignant melanoma from dysplastic nevus. The aim of this research is to select the most efficient model of the SVM classifier for various image resolutions and to search for the best resolution-invariant wavelet bases. We show AUC as a function of the wavelet number and SVM kernels optimized by the Bayesian search for two independent data sets. Our results are compatible with the previous experiments to discriminate melanoma in dermoscopy images with ensembling and feed-forward neural networks.