A decomposable measure of inequality simply refers as a measure such that the variability of total inequality can be divided into two parts: ‘within inequality’ and ‘between inequalities’. By considering plural view of inequality measures (both absolute and relative) for two widely talked-about families of inequality measurement (Gini family and SD-CV family) in the literature, we propose that, variance (as an absolute measure in SD-CV family) is the most suitable measure for perfect decomposition of inequality. On the other hand, squared coefficient of variation (as a relative measure in SD-CV family) is far better measure for such purpose than Gini index (as a relative measure in Gini family) though they cannot be perfectly decomposed. An empirical study of a backward district of West Bengal is considered in order to analyse the effects of ‘within’ and ‘between’ components on inequality decomposition. Since one of the key points of inequality analysis is represented by the overlapping units, the effect of overlapping component on inequality decomposition is also considered.