Let (X, T) be a Cantor minimal system associated with a properly ordered Bratteli diagram with the equal path number property. In this paper we will show that there exists a Toeplitz flow (Y, S) such that (X, T) and (Y, S) are strongly orbit equivalent. This is an affirmative answer to the open problem in R. Gjerde and O. Johansen (Bratteli-Vershik models for Cantor minimal systems: applications to Toeplitz flows.