Machine for the manufacture of preforms (2) for plastic containers, comprising at least one station (10) for moulding the preforms and at least one apparatus (30) for injection of the plastic into the moulding station, comprising at least two stations (20) for cooling the preforms (2), symmetrically arranged with respect to the moulding station (10), there also being provided conveying means (50;150) movable with an alternating movement from the moulding station (10) to one of the two cooling stations (20) and vice versa for conveying the preforms (2) to the said cooling stations.