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

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... hich 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.