Pump for metering and dispensing a liquid or viscous product intended to be associated with a recipient containing said product, said pump having, at a so-called lower longitudinal end, an inlet aperture for the passage of the product coming from the recipient and, at a so-called upper longitudinal end, an outlet aperture for the dispensing of the product outside of the pump, said pump having inside a main chamber receiving a piston provided with a body and with a head, with said piston being mobile in the length of the main chamber, - said body having an internal duct passing through it in the lengthwise direction and connected to the inlet aperture at its lower portion for the flow of the product coming from said inlet aperture, - said body and the lower portion of said head of the piston occupying the main chamber by leaving empty only a separation chamber, arranged around the body of the piston, - said head of the piston fully separating, by an external flange, the separation chamber from a discharge chamber arranged in the vicinity of the outlet aperture, with the upper portion of said head having in its upper median portion a means for blocking said outlet aperture, with the internal duct at its upper end opening indirectly into the discharge chamber for the flow of the product in said chamber, with said discharge chamber having a variable volume according to the movement of the piston in the main chamber, - means for returning being provided to act on the piston by placing the means for blocking in the closed position of said outlet aperture, wherein the separation chamber is sealed to the flow of the product by not passing through the latter, wherein the means for blocking is the upper end of a punch extending between the upper end of the internal duct and the outlet aperture of the pump, with the punch having a rod and an upper end with a rounded or pointed shape; and wherein the punch has a passage for the product coming from the internal duct by being connected at its lower portion to said internal duct and at least one filling aperture opening into the discharge chamber for the flow of said product in the discharge chamber and wherein the passage is carried out by a longitudinal groove starting from the lower portion of the punch facing the internal duct and communicating in a sealed manner with said duct, with at least one portion of the groove forming a slot on the periphery of the punch, with this slot also serving as a filling aperture and wherein the longitudinal groove extends over the entire width of the punch, with two portions of the groove each forming a slot on the periphery of the punch, said slots being arranged opposite on said periphery, characterised in that a portion of the rod is surrounded by an inner flange, with a remaining portion of the and the upper end with rounded or pointed shape of the punch projecting upwardly from said inner flange, said inner flange being surrounded by the outer flange by leaving a space between them, with the punch and said flanges (13, 14) forming the head of the piston, the inner flange having an upper tapered portion narrowing to the remaining portion of the rod of the punch, and in that the passage is located in the remaining portion of the rod of the punch. - said body having an internal duct passing through it in the lengthwise direction and connected to the inlet aperture at its lower portion for the flow of the product coming from said inlet aperture, - said body and the lower portion of said head of the piston occupying the main chamber by leaving empty only a separation chamber, arranged around the body of the piston, - said head of the piston fully separating, by an external flange, the separation chamber from a discharge chamber arranged in the vicinity of the outlet aperture, with the upper portion of said head having in its upper median portion a means for blocking said outlet aperture, with the internal duct at its upper end opening indirectly into the discharge chamber for the flow of the product in said chamber, with said discharge chamber having a variable volume according to the movement of the piston in the main chamber, - means for returning being provided to act on the piston by placing the means for blocking in the closed position of said outlet aperture,