A v-path of an arc xy in a multipartite tournament T is an oriented oath in T-y which starts at x such that y does not dominate and end vertex of the path. We show that if T is a regular n-partite (n$geq$7) tournament, then every arc of T has a v-path of length m for all m satisfying 2$leq$m$leq$n-2. Our result extends the corresponding result for regular tournaments, due to Alspach, Reid and Roselle [2] in 1974, to regular multipartite tournaments.