The problem of constructing composite indices has most often been tackled by using principal components in several disciplines. The approach, however, has some vital weaknesses. The paper suggests a method of constructing composite indices based upon full information contained in the data set. The method is also free from major defects of the method of principal components. The proposed method is amenable to simple statistical tests and provides a natural extension of the concept of centroid to statistically dependent constituent variables. The method is definitely a better substitute of the methods of principal components and factor analysis.