A machine (100) for making filter bags (1) for infusion products, the machine (100) being of the type comprising, one after the other along a production line (P), a plurality of operating stations designed to form the filter bags (1) and at least one operating outfeed station (7) for handling the filter bags (1) made; the operating outfeed and handling station (7) comprises conveying means (8) designed to successively pick up and withhold the filter bags (1) along a certain section (T1) of the line (P); supporting guide means (9) along which an ordered and continuous succession of filter bags (1) is formed and fed along another section (T2) of the line (P); and means (11) for picking up and transferring the filter bags from the conveying means (8) to the supporting guide means (9).