A fuel injector of the multipoint type, intended to be mounted in an injection system of a combustion chamber, comprising: - an arm for supplying fuel, - a first ferrule comprising a part forming a connection in which is housed one end of the arm and a part forming a body which is open internally, having an external diameter, and perforated internally with channels (342p, 342m) for circulating fuel communicating with the supply arm, - at least one swirler stage (31, 31a) interlocked in the opening of the body of the first ferrule, - a fuel injection nozzle housed in a part forming the hub of the swirler stage to inject fuel originating from the inside of the pilot circulation channel of the first ferrule toward the axis I-I' of the injection system, - a second ferrule comprising a part forming a body which is open internally, having an external diameter and of which the periphery is perforated with multipoint injection channels to inject fuel toward the periphery of the injection system, the bodies (341, 350) of the first and second ferrules of the injector being interlocked such that their internal openings (01, 02) and external diameters (D1, D2) mutually overlap at least partially, defining a hollow volume comprising at least three concentric baffles (360, 361, 362) communicating with the circulation channels (342p, 342m), of which the central baffle opens out onto the multipoint injection channels and the other peripheral baffles (361, 362) are adapted to circulate fuel around the central baffle in order to cool the fuel supplying the multipoint injection channels, and then to supply the injection nozzle, The peripheral baffles (361, 362) opening in a fuel admission chamber characterized in that the baffles (360, 361, 362) are continuous and each communicate with at least one separate circulation channel (342p, 342m), the fuel admission chamber being arranged in a zone diametrically opposing the circulation channels (342p, 342m) and which communicates with the injection nozzle, in order to achieve uniform supply and cooling of the injector. - an arm for supplying fuel, - a first ferrule comprising a part forming a connection in which is housed one end of the arm and a part forming a body which is open internally, having an external diameter, and perforated internally with channels (342p, 342m) for circulating fuel communicating with the supply arm, - at least one swirler stage (31, 31a) interlocked in the opening of the body of the first ferrule, - a fuel injection nozzle housed in a part forming the hub of the swirler stage to inject fuel originating from the inside of the pilot circulation channel of the first ferrule toward the axis I-I' of the injection system, - a second ferrule comprising a part forming a body which is open internally, having an external diameter and of which the periphery is perforated with multipoint injection channels to inject fuel toward the periphery of the injection system, the bodies (341, 350) of the first and second ferrules of the injector being interlocked such that their internal openings (01, 02) and external diameters (D1, D2) mutually overlap at least partially, defining a hollow volume comprising at least three concentric baffles (360, 361, 362) communicating with the circulation channels (342p, 342m), of which the central baffle opens out onto the multipoint injection channels and the other peripheral baffles (361, 362) are adapted to circulate fuel around the central baffle in order to cool the fuel supplying the multipoint injection channels, and then to supply the injection nozzle,