Often in remote sensing applications, when using statistical classifiers, it is implicitly assumed that the training samples used to train a classifier represent the true classes. This assumption may not be valid for several reasons. First, it is unlikely that enough training samples will be available to accurately estimate the parameters of the class density functions. Second, samples from one class often come from adjacent areas on the ground, and so they are spectrally more similar than it can be expected from the entire class. Third, in the case where the classes are multimodal, the non-parametric density techniques are used that require many more training samples than parametric ones. Four, there is some evidence that the accuracy of a classifier tends to decrease near the boundaries between two classes where the sample is a mixture of two or more classes. The purpose of this paper is to propose a new method, based on evidential reasoning, in which the classification can be more reliable and accurate despite of an insufficiency and a poor quality of the training data. Using real data, the obtained results are satisfactory. The scheme outperforms the conventional statistical classifiers. It may be used for various applications with multisource data.