Abstract The Gini index of income inequality for grouped data, is decomposed into the between groups and the within groups inequality that arises between the subgroups. In case that the subgroup income ranges overlap, the decomposition of the Gini index obtains as the sum of three terms, the between groups index, the within group index and the residual term. In this study we propose a method for reducing the value of the Gini’s index residual term, in case of overlapping. The proposed method concerns the representation of Gini index as a matrix product. We study both the case of large subgroups and the case of small samples as well. Τhe accurate calculation of the Gini Index based on data grouped by categories, commonly arises with income data, that are usually grouped for confidentiality purposes. 1. INTRODUCTION A decomposable inequality measure is defined as a measure such that the total inequality of a population can be broken down into the inequality that existing within subgroups of the population and the inequality that existing between subgroups. Gini index of inequality can be expressed as a decomposable measure but in case that the subgroup income ranges overlap, the decomposition of the Gini index obtains as the sum of three terms, the between groups index, the within group index and the residual term. Our main goal in this study, is to propose a correction that reduces the value of the residual term. The correction concerns the inequality between groups and the inequality within groups. Τhe impact of the methodology is examined for both large and small subgroups. The second section describes the decomposition of the Gini index that obtains as a matrix product and the proposed methodology that leads to the correction of the Gini index while it reduces the value of the residual term and the small error bias. The third section contains the simulation results of the proposed method as well as the results based on official data. We calculate the residual term before and after the correction for small and large subgroups and we compare the results regarding the value of the residual term. We also calculate the standard error and the corresponding confidence intervals. The last section describes the conclusions and the contribution of the proposed method to the simulation data and to the official data