The present invention relates to a process for cracking a hydrocarbon feedstock in a steam cracker unit, comprising the following steps of: feeding a liquid hydrocarbon feedstock to a hydrocracking unit, separating the stream thus hydrocracked in said hydrocracking unit into a high content aromatics stream and a gaseous stream comprising C2-C4 paraffins, hydrogen and methane, separating C2-C4 paraffins from said gaseous stream, feeding said C2-C4 paraffins thus separated to the furnace section of a steam cracker unit.