Method for assembling at least two pieces of silicon carbide based materials by non reactive refractory brazing, wherein these pieces are put into contact with a non reactive brazing solder composition and the assembly formed by the pieces and the brazing solder composition is heated to a brazing temperature sufficient to fuse the brazing solder composition in order to form a refractory joint, in which the non reactive brazing solder composition is constituted, in atomic percentages, of from 40 to 97% silicon and of from 60 to 3% of another element chosen in the group consisting of chromium, rhenium, vanadium, ruthenium, iridium, rhodium, palladium, cobalt, platinum, cerium and zirconium and wherein, before brazing, a strengthening agent of SiC and/or C is added.Brazing solder composition, composition for refractory brazing. Refractory joint and assembly obtained by the method.