A paper sheet handling machine configured to handle a hybrid banknote having a paper portion and a predetermined material portion formed from a material other than paper, comprising: a transport unit configured to transport the hybrid banknote in a transport direction in which the hybrid banknote is transported by the transport unit; a recognition unit provided in the transport unit, the recognition unit being configured to detect a first position, in a width direction, of the predetermined material portion of the hybrid banknote transported by the transport unit, wherein the width direction is orthogonal to the transport direction; a detection unit provided in the transport unit, the detection unit being configured to detect the first position, in the width direction, of the predetermined material portion of the hybrid banknote transported by the transport unit; a storage unit (20, 30, 40) configured to store the hybrid banknote transported from the transport unit, the storage unit having a first specific member comprising a belt-shaped tape for winding the hybrid banknote onto an outer circumferential surface of a rotating member or the storage unit (30, 40) configured to store the paper sheet transported from the transport unit therein in a stacked state and having a second specific member (32, 42) comprising a pair of feed rollers for feeding, from the storage unit (30, 40), the hybrid banknote stored in the storage unit (30, 40); and a shifting unit provided between the detection unit and the recognition unit in the transport unit, the shifting unit being configured to shift the hybrid banknote being transported by the transport unit, in the width direction, according to a second position, in the width direction, of the first specific member or the second specific member (32, 42), respectively of the storage unit (20, 30, 40) such that the first position, in the width direction, of the predetermined material portion of the hybrid banknote to be stored in the storage unit at least partially overlaps the second position, in the width direction, of the first specific member of the storage unit, or such that the first position, in the width direction, of the predetermined material portion of each hybrid banknote to be stored in the storage unit (30, 40) is displaced from the second position, in the width direction, of the second specific member (32, 42) of the storage unit (30, 40) and the paper portion of the hybrid banknote overlaps the second specific member (32, 42), wherein a shift distance by which the hybrid banknote is shifted in the width direction by the shifting unit is calculated on the basis of a result of recognition by the recognition unit and a result of detection by the detection unit. a transport unit configured to transport the hybrid banknote in a transport direction in which the hybrid banknote is transported by the transport unit; a recognition unit provided in the transport unit, the recognition unit being configured to detect a first position, in a width direction, of the predetermined material portion of the hybrid banknote transported by the transport unit, wherein the width direction is orthogonal to the transport direction; a detection unit provided in the transport unit, the detection unit being configured to detect the first position, in the width direction, of the predetermined material portion of the hybrid banknote transported by the transport unit; a storage unit (20, 30, 40) configured to store the hybrid banknote transported from the transport unit, the storage unit having a first specific member comprising a belt-shaped tape for winding the hybrid banknote onto an outer circumferential surface of a rotating member or the storage unit (30, 40) configured to store the paper sheet transported from the transport unit therein in a stacked state and having a second specific member (32, 42) comprising a pair of feed rollers for feeding, from the storage unit (30, 40), the hybrid banknote stored in the storage unit (30, 40); and a shifting unit provided between the detection unit and the recognition unit in the transport unit, the shifting unit being configured to shift the hybrid banknote being transported by the transport unit, in the width direction, according to a second position, in the width direction, of the first specific member or the second specific member (32, 42), respectively of the storage unit (20, 30, 40) such that the first position, in the width direction, of the predetermined material portion of the hybrid banknote to be stored in the storage unit at least partially overlaps the second position, in the width direction, of the first specific member of the storage unit, or such that the first position, in the width direction, of the predetermined material portion of each hybrid banknote to be stored in the storage unit (30, 40) is displaced from the second position, in the width direction, of the second specific member (32, 42) of the storage unit (30, 40) and the paper portion of the hybrid banknote overlaps the second specific member (32, 42), wherein a shift distance by which the hybrid banknote is shifted in the width direction by the shifting unit is calculated on the basis of a result of recognition by the recognition unit and a result of detection by the detection unit.