In this article we consider a Brownian motion with drift, denoted by S = (St)t≥0, of the form dSt = μtdt+ dBt for t ≥ 0, with a specific non-trivial drift predictable with respect to F , the natural filtration of the Brownian motion B = (Bt)t≥0. We construct a process H = (Ht)t≥0 also predictable with respect to F B such that ((H · S)t)t≥0 is a Brownian motion in its own filtration. Furthermore...