The three conventional anthropometric indicators of childhood undernutrition are stunting (low height-for-age), underweight (low weight-for-age) and wasting (low weight-for-height). Recently a new composite index, namely the Composite Index of Anthropometric Failure (CIAF) has been proposed and utilised to study childhood undernutrition. In this paper, we have attempted to construct three new indices of undernutrition, relative to the CIAF. These three indices are: Stunting Index (SI) = Stunting / CIAF, Underweight Index (UI) = Underweight / CIAF and Wasting Index (WI) = Wasting / CIAF. Furthermore, we have calculated and compared these indices using our dataset as well as other existing datasets. Using our dataset, the sex-combined values of SI, UI and WI were 0.364, 0.866 and 0.684, respectively. The corresponding values among boys were 0.364, 0.866 and 0.729. Among girls, they were 0.380, 0.866 and 0.641, respectively. When applied to the all India dataset, the values of SI, UI and WI were 0.756, 0.788 and 0.266, respectively. Similar values (SI = 0.723, UI = 0.681, WI = 0.294) were observed when they were computed on data available from Coimbatore, South India. In conclusion, we suggest that these three new indices provide additional information on the prevalence of different forms of undernutrition relative to the total level of undernutrition in a particular population.