We present a proof for the quantile normalization method proposed by \citet{Bolstad-03} which has become one of the most popular methods to align density curves in microarray data analysis. We prove consistency of this method which is viewed as an application to density curve registration of the new method proposed in \citet{Dupuy-Loubes-Maza-11}, the structural expectation. Moreover, when this method fails in some case of mixture, we propose a new methodology to cope with this issue
