We present a detailed analysis together with exact numerical calculations on one-loop contributions to the branching ratio of the radiative decay of mu and tau, namely mu -> e gamma, tau -> e gamma, and tau ->mu gamma from supersymmetry without R parity, focusing on contributions involving bilinear couplings. A numerical study is performed to obtain explicit bounds on the parameters under the present experimental limit. We present, and use in the calculation, formulas for exact mass eigenstate effective couplings. In this sense, we present an exact analysis free from approximation for the first time. After comparing our results against the closest early analysis, we discovered a major difference in resulted constraints on some mu B-*(i)j combinations. Constraints from neutrino masses on the parameters were considered. Our result indicates that the branching ratio measurement on mu -> e gamma down to 10(-13)-10(-14) and beyond, as targeted by the MEG experiment, has a chance of observing decay from the R-parity violating scenario.