Classifying fingerprint images may require an important features extraction step. The scale-invariant feature transform which extracts local descriptors from images is robust to image scale, rotation and also to changes in illumination, noise, etc. It allows to represent an image in term of the comfortable bag-of-visual-words. This representation leads to a very large number of dimensions. In this case, random forest of oblique decision trees is very efficient for a small number of classes. However, in fingerprint classification, there are as many classes as individuals. A multi-class version of random forest of oblique decision trees is thus proposed. The numerical tests on seven real datasets (up to 5,000 dimensions and 389 classes) show that our proposal has very high accuracy and outperforms state-of-the-art algorithms.