We describe an improvement on Ukkonen's Enhanced Dynamic Programming (EHD) approximate string-matching algorithm for unit-penalty four-edit comparisons. The new algorithm has an asymptotic complexity similar to that of Ukkonen's but is significantly faster due to a decrease in the number of array cell calculations. A 42% speedup was achieved in an application involving name comparisons. Even greater improvements are possible when comparing longer and more dissimilar strings. Although the speed of the algorithm under consideration is comparable to other fast ASM algorithms, it has greater effectiveness in text-processing applications because it supports all four basic Damerau-type editing operations.