A feed table and a receiving table respectively having top surfaces which are flush with each other are positioned spaced from each other by a very small distance. A magnetic recording tape is fed along the top surface of the feed table toward the receiving table to extend over the top surface of the receiving table across the space between the tables, and is fixed to the top surfaces of the tables. A cutting edge is inserted into the space between the tables to cut the recording tape. A leader tape is fed along the top surface of the feed table toward the receiving table to extend over the top surface of the receiving table across the space between the tables by a predetermined length, and is fixed to the top surfaces of the tables. Then the cutting edge is inserted into the space to sever a leader tape piece having a predetermined length from the leader tape. The receiving table is moved with respect to the feed table in the lateral direction of the tapes so that the leader tape piece held on the receiving table is aligned with the part of the recording tape held on the feed table. Further the receiving table is moved in the longitudinal direction of the tapes to adjust the space between the opposed ends of the leader tape piece and the recording tape to an optimal value, and subsequently a splicing tape piece is applied to the opposed end portions of the leader tape piece and the recording tape.