The authors study a problem of classification of four-letter words which arises in the study of DNA sequences in biology. Precisely, they consider the equivalence relation on the set of all words on the four-letter alphabet $\{-2,-1,1,2\}$ generated by the usual conjugacy and the reverse complementation; this last mapping is the composition of the reversal (taking the mirror image) and the letterwise complementation (taking the opposite of every symbol). \par They give enumeration formulas for the number of equivalence classes for the previous relation as a function of the length; moreover, they are able to assign a distinguished word to each conjugacy class. \par To achieve these goals, the authors use a mapping between four-letter words and two-letter words of double length. For two-letter words, they introduce the concept of a lexical word, which is based on a precise total order relation on words (something like the definition of Lyndon words from the usual lexicographical order). Their order is related to the usual order on functions, when two-letter words are used in a certain way to define mappings from the unit interval into itself. \par Primitive words are of special interest in this paper and Möbius inversion formulas are a basic tool to solve the enumeration problem.