This paper systematises the method initiated by Burtless (1999) and provides a general framework for decomposing inequality by factor components. It has the double advantage over usual decomposition procedures to allow for a decomposition of changes in the whole income distribution and to distinguish between the effect of marginal distribution changes of income sources and that of changes in correlation between income sources. An illustration is provided for Taiwan, which emphasises the central role played by changes in assortative mating of spouses.