In this paper we introduce the V -transform (V -BWT), a variant of the classic Burrows–Wheeler Transform. The original BWT uses lexicographic order, whereas we apply a distinct total ordering of strings called V -order. V -order string comparison and Lyndonlike factorization of a string x = x[1..n] into V -words have recently been shown to be linear in their use of time and space (Daykin et al., 2011). Here we apply these subcomputations, along with Θ(n) suffix-sorting (Ko and Aluru, 2003), to implement linear V -sorting of all the rotations of a string. When it is known that the input string x is a V -word, we compute the V -transform in Θ(n) time and space, and also outline an efficient algorithm for inverting the V -transform and recovering x. We further outline a bijective algorithm in the case that x is arbitrary. We propose future research into other variants of transforms using lex-extension orderings (Daykin et al., 2013). Motivation for this work arises in possible applications to data compression.