A sizing composition for reinforcing fibres is provided which makes it possible to improve the adhesion of these fibres with respect to an organic matrix that forms, with them, a part made of a composite material and that results from the chain transfer polymerization of a curable resin. The sizing composition includes a polybutadiene prepolymer comprising at least two epoxide functions, a cross-linking agent comprising at least two reactive functions, at least one of which is a thiol function; and a catalyst comprising at least one tertiary amine function.