Standard techniques of indirect estimation of child mortality use data from summary birth histories consisting of only two questions - number of children ever born alive and the number of children dead. However the estimation is based on several assumptions about fertility and mortality patterns, and rates computed for recent periods are biased. We propose and apply an innovative approach based on imputation of full birth histories onto summary birth histories. The resulting imputed full birth history is used to calculate child mortality rates using standard life table procedures. We apply the approach to data from the Malawi 2008 Population Census and the 2004 and 2010 Demographic and Health Survey datasets. Preliminary results are promising, with most of the imputed child mortality rates falling within the 95% confidence intervals of the rates directly computed from the 2010 DHS survey. In addition, choice of the existing full birth history data for the imputation did not appear to affect the resulting mortality rates computed from the imputed full birth history data.