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A rapid reduction in under-five mortality has put Bangladesh on-track to reach Millennium Development Goal 4. Little research, however, has been conducted into neonatal reductions and sub-national rates in the country, with considerable disparities potentially masked by national reductions. The aim of this paper is to estimate national and sub-national rates of neonatal mortality to compute relative and absolute inequalities between sub-national groups and draw comparisons with rates of under-five mortality. Mortality rates for under-five children and neonates were estimated directly for 1980-1981 to 2010-2011 using data from six waves of the Demographic and Health Survey. Rates were stratified by levels of rural/urban location, household wealth and maternal education. Absolute and relative inequalities within these groups were measured by rate differences and ratios, and where possible, slope and relative indices of inequality. National mortality was shown to have decreased dramatically although at differential rates for under-fives and neonates. Across all equity markers, a general pattern of declining absolute but constant relative inequalities was found. For mortality rates stratified by education and wealth mixed evidence suggests that relative inequalities may have also fallen. Although disparities remain, Bangladesh has achieved a rare combination of substantive reductions in mortality levels without increases in relative inequalities. A coalescence of substantial increases in coverage and equitable distribution of key child and neonatal interventions with widespread health sectoral and policy changes over the last 30 years may in part explain this exceptional pattern. [ABSTRACT FROM AUTHOR]