In this work, a theoretical study of new polymorphic varieties of boron nitride, which have diamond-like structures with boron and nitrogen atoms in equivalent structural positions, was carried out. The model construction of new phases of boron nitride was performed in the process of crosslinking precursor nanostructures. Single-walled boron nitride nanotubes with chirality indices (3;0), (4;0), and (6;0) were chosen as precursors for the model construction of diamond-like phases. Using the density functional theory method in the generalized gradient approximation, the possibility of stable existence of three new structural varieties of boron nitride with a diamond-like structure was established: BN-TA4, BN-TA5, BN-TA6. The structure of the BN-TA7 diamond-like phase turned out to be unstable and, in the process of geometric optimization, was transformed into the initial structure, a boron nitride nanotube (6;0). As a structural characteristic, the bulk density of the new polymorphs was determined, which is in the range from 2.613 to 3.0836 g/cm3. The sublimation energy of new polymorphic varieties ranges from 17.16 to 17.63 eV/(BN). The value of the band gap near the Fermi energy varies from 5.37 to 5.74 eV.