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We present a design of a 400-MHz/60-mm all-REBCO nuclear magnetic resonance (NMR) magnet (H400) that consists of a stack of 56 double-pancake (DP) coils. With the multiwidth no-insulation technique incorporated, DP coils were wound with REBCO tapes of five different widths, i.e., 4.1, 5.1, 6.1, 7.1, and 8.1 mm; DP coils placed at and near the magnet midplane were wound with the narrowest (4.1 mm wide) REBCO tapes, whereas those with progressively wider tapes were placed toward the top and bottom of the magnet, where the "perpendicular field B ⊥ " is at its peak within the magnet. The magnet was designed to be operated under a conduction cooling environment at 20 K. Once successfully completed, the magnet will be installed as an NMR user facility in the Korea Basic Science Institute. Basic magnet performances and major technical challenges were discussed.