Method for implementing an operation of a high bay storage unit with a plurality of rows of shelves (14, 16, 18) and with a plurality of storage locations, which can be optionally filled with a plurality of storage objects, with: - forming at least one moving out path (x) between a storage location of the high bay storage unit and at least one exit (y) arranged transversely to the moving out path (x), wherein the moving out path (x) is arranged between two rows of shelves (14, 16, 18), - conveying at least one storage object which is storable in the high bay storage unit in a storage location by means of a reciprocating device along the moving out path (x) to the exit (y), - caching the at least one storage object in between the conveying transversely to the moving out path (x) adjacent to the exit (y) in storage places at a caching location in the high bay storage unit, starting from the reciprocating device along an introducing direction to the caching location, - removing a plurality of storage objects from the caching location by means of a conveying means which is movable along the exit (y) and which is actuable independently of the reciprocating device and which has at least one conveying auxiliary device for selectively picking at least one of the storage objects located at the individually accessible storage locations in the caching location transversely to the exit and also transversely to the introducing direction to the caching location and in the desired order for sequencing the storage objects already at the conveying means in the high bay storage unit without rearrangement of the storage objects, - conveying the storage objects on the conveying means in sequenced order out of the high bay storage unit. - forming at least one moving out path (x) between a storage location of the high bay storage unit and at least one exit (y) arranged transversely to the moving out path (x), wherein the moving out path (x) is arranged between two rows of shelves (14, 16, 18), - conveying at least one storage object which is storable in the high bay storage unit in a storage location by means of a reciprocating device along the moving out path (x) to the exit (y), - caching the at least one storage object in between the conveying transversely to the moving out path (x) adjacent to the exit (y) in storage places at a caching location in the high bay storage unit, starting from the reciprocating device along an introducing direction to the caching location, - removing a plurality of storage objects from the caching location by means of a conveying means which is movable along the exit (y) and which is actuable independently of the reciprocating device and which has at least one conveying auxiliary device for selectively picking at least one of the storage objects located at the individually accessible storage locations in the caching location transversely to the exit and also transversely to the introducing direction to the caching location and in the desired order for sequencing the storage objects already at the conveying means in the high bay storage unit without rearrangement of the storage objects, - conveying the storage objects on the conveying means in sequenced order out of the high bay storage unit.