The electrical transport properties of a four-layered hydrogen-terminated cubic boron nitride sub-nanometer film in contact with gold electrodes are investigated via density functional calculations. The sample exhibits asymmetric metallic surfaces, a fundamental feature that triggers the system to behave like a typical p-n junction diode for voltage bias in the interval -0.2 ≤ V ≤ 0.2, where a rectification ratio up to 62 is verified. Further, in the wider region -0.3 ≤ V ≤ 0.3, negative differential resistance with a peak-to-valley ratio of 10 is observed. The qualitative behavior of the I-V characteristics is described in terms of the hydrogenated cBN film equilibrium electronic structure. Such a film shows metallic surfaces due to surface electronic states at a fraction of eV above and below the Fermi level of the N-H terminated and B-H terminated surfaces, respectively, with a wide bulk-band gap characteristic of BN materials. Such a mechanism is supported by transmission coefficient calculations, with the Landauer-Büttiker formula governing the I-V characteristics.