In order to produce both an olefinic fraction and a composition of diacids or diesters of fats, a process is carried out which comprises, in succession: a) metathesis of an unsaturated fat with ethylene in the presence of at least one non-aqueous ionic liquid; b) separating and recycling the ionic liquid used in the first step; c) separating, by distillation, the olefinic fraction (fraction A) from the unsaturated fat mono-ester or mono-basic acid fraction (fraction B) formed in step a); d) homometathesis of the mono-unsaturated fat ester or acid cut (fraction B) which allows the co-production of unsaturated fat diesters or diacids (fraction C) and ethylene which is recycled to the first methathesis step of the process; and e) optionally, recycling the ionic liquid containing the catalyst used in step d). Of particular application to an oleic sunflower oil, an oleic rapeseed oil or to a mixture of mono-alcohol esters of said oils, whereupon the process can produce both an olefinic fraction (mainly composed of 1-decene) and a composition of diesters or diacids wherein, in general, over half of the chains is constituted by unsaturated C18 chains (mainly composed of octadecene-9 1,18-iacid or diester) and to recycle the ethylene employed.