A new computer-aided diagnosis (CAD) system for detecting malignant melanoma from dermoscopy images based on a fixed grid wavelet network (FGWN) is proposed. This novel approach is unique in at least three ways: (i) the FGWN is a fixed WN which does not require gradient-type algorithms for its construction, (ii) the construction of FGWN is based on a new regressor selection technique: D-optimality orthogonal matching pursuit (DOOMP), and (iii) the entire CAD system relies on the proposed FGWN. These characteristics enhance the integrity and reliability of the results obtained from different stages of automatic melanoma diagnosis. The DOOMP algorithm optimises the network model approximation ability rapidly while improving the model adequacy and robustness. This FGWN is then used to build a CAD system, which performs image enhancement, segmentation, and classification. To classify the images, in the first stage, 441 features with respect to colour, texture, and shape of each lesion are extracted. By means of feature selection, these 441 features are then reduced to 10. The proposed CAD system achieved an accuracy of 91.82%, sensitivity of 92.61%, specificity of 91%, and area under the curve value of 0.944 on a challenging set of 1039 dermoscopy images.