The Lévy transform of a Brownian motion B is the Brownian motionB(1) given by Bt(1) = ∫0tsgn(Bs)dBs; callB(n) the Brownian motion obtained fromB by iterating n times this transformation. Weestablish that almost surely, the sequence of paths (t → Bt(n))n⩾0isdense in Wiener space, for the topology of uniform convergence on compact timeintervals.