The simultaneous use of multiple classifiers has been shown to provide performance improvement in classification problems. The selection of an optimal set of classifiers is an important part of multiple classifier systems and the independence of classifier outputs is generally considered to be an advantage for obtaining better multiple classifier systems. In this paper, the need for the classifier independence is interrogated from classification performance point of view. The performance achieved with the use of classifiers having independent joint distributions is compared to some other classifiers which are defined to have best and worst joint distributions. These distributions are obtained by formulating the combination operation as an optimization problem. The analysis revealed several important observations about classifier selection which are then used to analyze the problem of selecting an additional classifier to be used with the available multiple classifier system. (C) 2002 Pattern Recognition Society. Published by Elsevier Science Ltd. All rights reserved.