Drawing on the literature on poverty measurement, we suggest the application of the mean of squared deprivation gaps (MSDG), which captures the dimensions of level, depth and severity, as an alternative index of undernutrition. The application of this index can be intuitively justified by the biomedical finding that as nutritional shortfall increases, the physiological risks increase at an increasing rate. We have shown how we can analyze group inequality in nutritional deprivation among children using the subgroup consistency feature of the MSDG. Computing the MSDG (alternatively the share in total MSDG) for each wealth quintile, we have obtained CIMSDG, the concentration index based on MSDG among children in each of the major states of India. It may so happen that socioeconomic inequality in the level of undernutrition is abated but that in undernutrition, defined as a composite notion increases. The scenario of child underweight across wealth quintiles in some states depicts such a situation.