The invention relates to a method for synthesising a mercaptan from a terminal olefin and hydrogen sulphide which comprises the following consecutive steps: A—catalytic addition of hydrogen sulphide to a terminal olefin catalysed by an acid catalyst; B—separation of the products of the addition reaction into a light fraction including the surplus hydrogen sulphide and the olefins, and into a heavy fraction including at least one mercaptan and optionally one or more thioethers; C—a finishing step of passing the light fraction obtained in step B over an acid catalyst; then D—separation of the products of the finishing step into a fraction that is rich in hydrogen sulphide and into a fraction that is rich in additives; and finally E—recirculation of the fraction that is rich in hydrogen sulphide to the catalytic addition step A. The invention also relates to the facility for implementing said method.
