Fifth-generation (5G) mobile communication systems employ beamforming technology using massive multiple-input and multiple-output (MIMO) to improve the reception quality and spectrum efficiency within a cell. Meanwhile, coordinated beamforming among multiple base stations is an effective approach to improving the spectrum efficiency at the cell edges, in which massive MIMO is deployed at geographically distant base stations and beamforming control is conducted in a cooperative manner. Codebook-based beamforming is a method for realizing multi-cell coordinated beamforming, in which each base station selects one of multiple beams that are predefined in a codebook. In codebook-based beamforming, it is important to design an efficient codebook that takes into account the beam allocation and the number of beams. In general, the larger the number of beams defined in a codebook, the more finely tuned the beam control can be and a greater improvement in spectrum efficiency can be expected. However, it requires a huge signal processing to optimize the beam combinations with a large number of beams by coordinated beamforming. This paper proposes a novel codebook design that efficiently assigns beam directions and widths in a vertical plane. Computer simulations showed that the proposed codebook performs as well as the conventional method while requiring fewer beam combinations.