A process for production, from an olefinic C4 fraction, on the one hand, of high-purity isobutene and, on the other hand, of propylene by metathesis is described. The process comprises three successive stages: 1) the selective hydrogenation of butadiene with isomerization of butene-1 into butene-2 up to thermodynamic equilibrium; 2) the separation by isobutene at the column head that integrates the hydroisomerization of n-butenes, allowing a butene-2 fraction at the bottom, and 3) the metathesis of the butene-2 fraction with ethylene. By this process, it is possible to produce in a very selective way high-purity isobutene and polymerization-quality propylene.