Pump for dispensing a fluid product, comprising a piston (1) secured to an actuating rod (2) and sliding in a pump body (3) comprising a pump chamber defined between an inlet valve (11) and an outlet valve (12), said outlet valve (12) comprising an outlet valve element (39; 35), in which pump, upon actuation, said outlet valve element (39; 35) slides in fluidtight manner in the pump body (3), said pump body (3) comprising passage means (40) formed by at least part of the pump body of a greater internal diameter so that at the end of pump actuation said outlet valve element (39, 35) collaborates in a non‑fluidtight manner with said passage means (40) in order to open said outlet valve (12) to allow the product contained in the pump chamber to be expelled.