A machine for making filter bags for infusion products starting from pieces of filtering material each having at least two free ends (1d, 1f), forming a head and a base of the piece of filtering material, with interposed at least one chamber containing a dose of product; the pieces feeding along a feed line, the machine comprising at least: - a first movement carousel for continuous rotary movement about a first axis of rotation and having at least a plurality of first operating stations positioned along, and continuously movable with, the first movement carousel, each first operating station being configured to retain and operate on a corresponding piece of filtering material fed along at least one predetermined angular stretch of rotation of the first movement carousel, to obtain at least a lifting of the chamber to an upright position, that is to say, positioned radially relative to the first axis of rotation; - a second movement carousel rotatable continuously about a second axis parallel to the first axis of rotation; - a transfer means which are configured to transfer the pieces of filtering material from the first movement carousel to thesecond movement carousel; the transfer means comprising a first wheel, which is rotatable continuously about a third axis of rotation parallel to the first and to the second axis of rotation in a synchronised fashion with the first movement carousel and the second movement carousel; the first wheel comprising a plurality of receiving units positioned along, and able to move continuously with, the first wheel for receiving from the corresponding first operating stations of the first movement carousel, and releasing on the second movement carousel, a corresponding piece of filtering material being formed after a predetermined arc of rotation; each receiving unit comprising first gripping and stabilising means (8, 13) for retaining the piece of filtering material upright and positioned with the free head end towards the third axis of rotation; the gripping and stabilising means (8, 13) comprising stabilising means for stabilising the piece of filtering material in an upright position at the receiving of the piece of filtering material, wherein the stabilising means of each receiving unit comprises a first gripper consisting of two fork-shaped claws (8a, 8b) for retaining the piece of filtering material and articulated on the receiving unit; each first gripper being configured to rotate between an open operating position for gripping or releasing the piece of filtering material, wherein the two claws (8a, 8b) are spaced apart from each other, and a closed operating position for retaining the piece of filtering material, wherein the two claws (8a, 8b) are moved towards each other, characterised in that the fork-shaped claws (8a, 8b) of the first gripper have corresponding pairs of end heads (22, 23) each having a transversal tab for retaining the lateral edges of the piece of filtering material and configured for defining a free central zone from the base end to the head end of the piece of filtering material. - a first movement carousel for continuous rotary movement about a first axis of rotation and having at least a plurality of first operating stations positioned along, and continuously movable with, the first movement carousel, each first operating station being configured to retain and operate on a corresponding piece of filtering material fed along at least one predetermined angular stretch of rotation of the first movement carousel, to obtain at least a lifting of the chamber to an upright position, that is to say, positioned radially relative to the first axis of rotation; - a second movement carousel rotatable continuously about a second axis parallel to the first axis of rotation; - a transfer means which are configured to transfer the pieces of filtering material from the first movement carousel to thesecond movement carousel; the transfer means comprising a first wheel, which is rotatable continuously about a third axis of rotation parallel to the first and to the second axis of rotation in a synchronised fashion with the first movement carousel and the second movement carousel; the first wheel comprising a plurality of receiving units positioned along, and able to move continuously with, the first wheel for receiving from the corresponding first operating stations of the first movement carousel, and releasing on the second movement carousel, a corresponding piece of filtering material being formed after a predetermined arc of rotation; each receiving unit comprising first gripping and stabilising means (8, 13) for retaining the piece of filtering material upright and positioned with the free head end towards the third axis of rotation; the gripping and stabilising means (8, 13) comprising stabilising means for stabilising the piece of filtering material in an upright position at the receiving of the piece of filtering material,