We study algebraic conditions when a pseudo MV-algebra is an interval in thelexicographic product of an Abelian unital $ell$-group and an $ell$-groupthat is not necessary Abelian. We introduce $(H,u)$-perfect pseudo MV-algebrasand strong $(H,u)$-perfect pseudo MV-algebras, the latter ones will have arepresentation by a lexicographic product. Fixing a unital $ell$-group$(H,u)$, the category of strong $(H,u)$-perfect pseudo MV-algebras iscategorically equivalent to the category of $ell$-groups.
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