A process for treating a feedstock from a renewable source, comprising the following stages: a) hydrotreatment in the presence of a fixed-bed catalyst, said catalyst comprising a hydrodehydrogenizing function and an amorphous support, at a temperature ranging between 200°C and 450°C, at a pressure ranging between 1 MPa and 10 MPa, at an hourly space velocity ranging between 0.1 h -1 and 10 h -1 and in the presence of a total amount of hydrogen mixed with the feedstock such that the hydrogen/feedstock ratio ranges between 150 and 750 Nm 3 hydrogen/m 3 feedstock, b) separtion, from the effluent from stage a), of at least part of the water and at least one hydrocarbon-containing base, c) removal of the nitrogen compounds from said hydrocarbon-containing base from stage b), d) hydroisomerization of a least part of said hydrocarbon-containing base from stage c) in the presence of a fixed-bed hydroisomerization selective catalyst, said catalyst comprising at least one metal of group VIII and/or at least one metal of group VIB and at least one monodimensional 10 MR zeolite molecular sieve selected from the zeolite molecular sieves ZSM-48 and ZBM-30, alone or in admixture,, wherein said stage c) is carried out at a temperature ranging between 150°C and 500°C, at a pressure ranging between 1 MPa and 10 MPa, at an hourly space velocity ranging between 0.1 h -1 and 10 h -1 and in the presence of a total amount of hydrogen mixed with the feedstock such that the hydrogen/feedstock ratio ranges between 70 and 1000 Nm 3 /m 3 feedstock, e) separation, from the effluent from stage d), of the hydrogen, the gases and at least one diesel fuel base. a) hydrotreatment in the presence of a fixed-bed catalyst, said catalyst comprising a hydrodehydrogenizing function and an amorphous support, at a temperature ranging between 200°C and 450°C, at a pressure ranging between 1 MPa and 10 MPa, at an hourly space velocity ranging between 0.1 h -1 and 10 h -1 and in the presence of a total amount of hydrogen mixed with the feedstock such that the hydrogen/feedstock ratio ranges between 150 and 750 Nm 3 hydrogen/m 3 feedstock, b) separtion, from the effluent from stage a), of at least part of the water and at least one hydrocarbon-containing base, c) removal of the nitrogen compounds from said hydrocarbon-containing base from stage b), d) hydroisomerization of a least part of said hydrocarbon-containing base from stage c) in the presence of a fixed-bed hydroisomerization selective catalyst, said catalyst comprising at least one metal of group VIII and/or at least one metal of group VIB and at least one monodimensional 10 MR zeolite molecular sieve selected from the zeolite molecular sieves ZSM-48 and ZBM-30, alone or in admixture,, wherein said stage c) is carried out at a temperature ranging between 150°C and 500°C, at a pressure ranging between 1 MPa and 10 MPa, at an hourly space velocity ranging between 0.1 h -1 and 10 h -1 and in the presence of a total amount of hydrogen mixed with the feedstock such that the hydrogen/feedstock ratio ranges between 70 and 1000 Nm 3 /m 3 feedstock, e) separation, from the effluent from stage d), of the hydrogen, the gases and at least one diesel fuel base.