The invention describes a process for treatment of a feedstock that is obtained from a renewable source that comprises a hydrotreatment stage in the presence of at least one fixed-bed catalyst, whereby said catalyst comprises a hydro-dehydrogenating function and an amorphous substrate, at a temperature of between 50 and 450° C., at a pressure of between 1 MPa and 10 MPa, at an hourly volumetric flow rate of between 0.1 h−1 and 10 h−1, and in the presence of a total quantity of hydrogen that is mixed with the feedstock such that the hydrogen/feedstock ratio is between 50 and 1000 Nm3 of hydrogen/m3 of feedstock, followed by a separation from the hydrotreated effluent that is obtained from stage a) of hydrogen, gases, and at least one liquid hydrocarbon effluent that consists of at least 50% linear n-paraffins, and a steam-cracking of at least one portion of the liquid hydrocarbon effluent that is obtained from stage b).