Classification of imbalanced data is a challenging issue in the interpretation of remote sensing images. In a majority class (negatives), there are much more pixels than in a minority class (positives). This imbalanced data makes the classification extremely difficult to produce higher accuracy. The sampling technique is one of techniques, which work well for many pattern data, but not for remote sensing images. The Fast Box algorithm (FBA) which uses the clustering algorithm was then proposed to characterize and discriminate the minority class from the majority class by determining the decision boundaries of the minority data. The FBA performs well in most pattern datasets; however, it fails to recognize the minority class properly in remote sensing images. In this study, we propose a new Constrained Box Algorithm (CBA), which can effectively detect the minority class within remote sensing images. The FBA often misclassifies negatives as positives, CBA eliminates this issue by restricting the maximum number of allowed positives within a box. Our new algorithm finds the minority class by an iterative process of discovering appropriate boundaries using clustering and eliminating majority instances from initial boundaries. A threshold is used to guide the search process to find acceptable boundaries. The set of accepted boundaries are then used to discover the minority class. Experimental results demonstrates that the minority class was correctly detected in satellite images.