Some spaces, such as compact Hausdorff spaces, have the property that every regular continuous image is normal. We look at such spaces. In particular, it is shown that if a normal space has finite Stone-Čech remainder, then every continuous image is normal. A consequence is that every continuous image of a Dedekind complete linearly ordered topological space of uncountable cofinality and coinitiality is normal. The normality of continuous images of other ordered spaces is also discussed.