A head part module consisting, together with a pump part module for mounting on a container body, of a discharge pump for a discharge container, the head part module comprising: a mounting cap having a link cylinder upwardly extending from an upper end of a mounting cylinder via an inward flange for fitting onto an outer face of a neck portion of the container body; a cover ring having a top plate with a through hole in the middle part thereof, an outer wall hanging from an outer circumference of the top plate and an internal first fitting strip as well as an external second fitting strip circumferentially provided on the rear face of the top plate, the link cylinder being rotatably fitted into the second fitting strip; and a push down head having an outer cylinder hanging from an outer circumference of a top plate, a first communication tube hanging from a rear face of the top plate above the through hole and a nozzle forwardly projecting from the outer cylinder, the outer cylinder 40 being detachably fitted onto an outer face of the outer wall; wherein the first fitting strip of the cover ring can be fitted onto an upper end of a pump cylinder of the pump part module and a first communication tube of the push down head is fitted onto a second communication tube serving also as a stem of the pump part module, respectively, by pushing down the head part module characterized in that the first fitting strip and the second fitting strip are formed as inner and outer fitting strip grooves divided by a middle wall hanging from the rear face of the top plate, and a second engagement strip and a first engagement strip are circumferentially provided on opposing circumferential faces of the second fitting strip 30 and the link cylinder to prevent removal of the link cylinder 10 by a mutual engagement. a mounting cap having a link cylinder upwardly extending from an upper end of a mounting cylinder via an inward flange for fitting onto an outer face of a neck portion of the container body; a cover ring having a top plate with a through hole in the middle part thereof, an outer wall hanging from an outer circumference of the top plate and an internal first fitting strip as well as an external second fitting strip circumferentially provided on the rear face of the top plate, the link cylinder being rotatably fitted into the second fitting strip; and a push down head having an outer cylinder hanging from an outer circumference of a top plate, a first communication tube hanging from a rear face of the top plate above the through hole and a nozzle forwardly projecting from the outer cylinder, the outer cylinder 40 being detachably fitted onto an outer face of the outer wall; wherein the first fitting strip of the cover ring can be fitted onto an upper end of a pump cylinder of the pump part module and a first communication tube of the push down head is fitted onto a second communication tube serving also as a stem of the pump part module, respectively, by pushing down the head part module characterized in that the first fitting strip and the second fitting strip are formed as inner and outer fitting strip grooves divided by a middle wall hanging from the rear face of the top plate, and a second engagement strip and a first engagement strip are circumferentially provided on opposing circumferential faces of the second fitting strip 30 and the link cylinder to prevent removal of the link cylinder 10 by a mutual engagement.