  We consider a stochastic linear transport equation with a globally H\"{o}lder
continuous and bounded vector field. Opposite to what happens in the
deterministic case where shocks may appear, we show that the unique solution
starting with a C^{1}-initial condition remains of class $C^{1}$ in space. We
also improve some results of Flandoli-Gubinelli-Priola (2009) about
well-posedness. Moreover, we prove a stability property for the solution with
respect to the initial datum.
