We present a new method of bias correction for deriving reliable Tully-Fisher distances in a magnitude or diameter selected sample of field galaxies. This normalized distance method (NDM) is first presented in a theoretical way using the formalism of bayesian statistics and is further applied to three different Tully-Fisher samples corresponding to three different passbands in B, I and r. Constraints imposed by the method, and influences of underlying assumptions and measurement errors are discussed in detail. A main feature of the methodology is to extract an unbiased subsample from the parent sample. We show that by taking into account all the components influencing the bias at a given distance, the NDM method allows to extend the unbiased range and to analyze peculiar velocities of galaxies within a sphere out to 8000 km.s$^{-1}$ around the Local Group. Finally, thanks to this tool, we show first evidences for both frontside and backside large amplitude infall toward the Perseus-Pisces supercluster. The strong convergent flow expected in the Great Attractor region is not confirmed, even if infall centers are detected in this direction. The observed velocity field rather corresponds to the cumulative pull of several clusters present in this sky area.