A method for removing a residual fluid contained in at least one external service hose associated to a high-pressure or low-pressure fluid, which is designed to connect a refrigerant recharging/recovering machine for recharging/recovering a refrigerant into/from an vehicle air-conditioning system; said refrigerant recharging/recovering machine comprising: - a main hydraulic circuit provided with at least one first external connector , connected to which is a first end of said external service hose ; said external service hose having a second free end structured to be coupled in a stable, but easily removable, way to a connector of said vehicle air-conditioning system; - refrigerant-recovery means , which comprise an inlet terminal connected to said main hydraulic circuit for receiving, through the latter, the refrigerant contained in the vehicle air-conditioning system, and are configured to filter the refrigerant from additional fluids to supply the filtered refrigerant itself to a tank ; and - at least one external auxiliary connector , connected to said inlet terminal of said refrigerant-recovery means and structured to be coupled in a stable, but easily removable, way to said second free end of said external service hose ; said method being characterized in that it comprises the following steps: - manually coupling said second free end of said at least one service hose directly to the external auxiliary connector ; and - operating said refrigerant-recovery means to cause part of the refrigerant contained in said tank to pass through the main hydraulic circuit and to flow from said first external connector to said external auxiliary connector traversing exclusively said external service hose in such a way as to remove exclusively the residual fluid contained therein, so that the residual fluid of said external service hose is entrained by the refrigerant directly to said refrigerant-recovery means without passing through the other service hose . - a main hydraulic circuit provided with at least one first external connector , connected to which is a first end of said external service hose ; said external service hose having a second free end structured to be coupled in a stable, but easily removable, way to a connector of said vehicle air-conditioning system; - refrigerant-recovery means , which comprise an inlet terminal connected to said main hydraulic circuit for receiving, through the latter, the refrigerant contained in the vehicle air-conditioning system, and are configured to filter the refrigerant from additional fluids to supply the filtered refrigerant itself to a tank ; and - at least one external auxiliary connector , connected to said inlet terminal of said refrigerant-recovery means and structured to be coupled in a stable, but easily removable, way to said second free end of said external service hose ; - manually coupling said second free end of said at least one service hose directly to the external auxiliary connector ; and - operating said refrigerant-recovery means to cause part of the refrigerant contained in said tank to pass through the main hydraulic circuit and to flow from said first external connector to said external auxiliary connector traversing exclusively said external service hose in such a way as to remove exclusively the residual fluid contained therein, so that the residual fluid of said external service hose is entrained by the refrigerant directly to said refrigerant-recovery means without passing through the other service hose . <EOS>