  We compute one loop neutrino masses in the R-parity violating Minimal
Supersymmetric Model, including the bilinear R-parity violating masses in the
mass insertion approximation. To the order we calculate, our results are
independent of the Higgs-lepton basis choice. We have a variety of perturbative
parameters-gauge, yukawa and trilinear couplings, and R_p violating masses.
Their relative magnitudes determine which diagrams are relevant for neutrino
mass calculations. We find new loop diagrams which can be relevant and have
frequently been neglected in the past. For the Grossman-Haber neutral loop
contribution to the neutrino mass matrix we obtain explicit analytic results.
