The experimental measurement of B(b→sγ) imposes important constraints on the charged Higgs boson mass in the MSSM. If squarks are in the few TeV range, the charged Higgs boson mass in the MSSM must satisfy $m_{H^{\pm}} \gsim 440$ GeV. For lighter squarks, then light charged Higgs bosons can be reconciled with B(b→sγ) only if there is also a light chargino. In the MSSM if we impose mχ±1>90 GeV then we need $m_{H^{\pm}} \gsim 110$ GeV. We show that by adding bilinear R--Parity violation (BRpV) in the tau sector, these bounds are relaxed. The bound on mH± in the MSSM--BRpV model is $\gsim 340$ GeV for the the heavy squark case and $m_{H^{\pm}} \gsim 75$ GeV for the case of light squarks. In this case the charged Higgs bosons would be observable at LEP II. The relaxation of the bounds is due mainly to the fact that charged Higgs bosons mix with staus and they contribute importantly to B(b→s... [Leer más...]