A process for assembling at least two parts made from a composite material incorporating a ceramic or vitroceramic matrix reinforced by ceramic fibers. A continuous connection between these parts is achieved by approaching two of the parts along their respective edges to be assembled, forming a joint between the two parts by sewing with a tie or link of ceramic fibers from each of the parts to be assembled and heating the joints by a heating device employing a powerful and extremely localized heating until the two parts are welded together.