Automatic melanoma diagnosis is very important to lower the mortality rate by detecting the disease in earlier stages and accurate diagnosis. The main aim of this paper is to improve the classification accuracy of melanoma using a proposed novel color and texture feature descriptor. Initially, the skin lesion area of input dermoscopy image is segmented using a convolutional neural network-based U-Net algorithm. Then extract discriminate color, texture and combined color-texture features with the help of proposed Inter Neighbor Statistical Color Feature (INSCF), Inter Neighbor Mean Order Pattern (INMOP) and Inter Neighbor Statistical Color Mean Order Pattern (INSCMOP) by incorporating inter color channel values. This proposed feature descriptors are capable to discriminate the detailed information derived from spatial inter-chromatic texture patterns of different channels within a region. Finally, three classifiers namely, K-Nearest Neighbors (KNN), Random Forest (RF), and Support Vector Machine (SVM) are used to classify the skin lesion in a dermoscopic image as benign lesion or melanoma. Experimental results indicate that the proposed INSCMOP with Random Forest classifier achieves the highest classification performance based on accuracy of 93.27% for ISIC 2016 dataset, 86% for ISIC 2017 dataset and 92.31% for ISBI 2019 dataset. Moreover, comparing the proposed method with other systems shows that this approach has an excellent performance in melanoma classification. In this research, without any manual interaction, the classification process is performed in an automated way. It would set up a valuable assistance for dermatologist in clinical practice.